NBER WORKING PAPER SERIES
A GENERAL EQUILIBRIUM MODEL OF SOVEREIGN DEFAULT AND BUSINESS
CYCLES
Enrique G. Mendoza
Vivian Z. Yue
Working Paper 17151
http://www.nber.org/papers/w17151
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
June 2011
Earlier versions of this paper circulated under the title "A Solution to the Disconnect between Country
Risk and Business Cycles Theories." We thank Cristina Arellano, Mark Aguiar, Andy Atkeson, Fernando
Broner, Jonathan Eaton, Gita Gopinath, Jonathan Heathcote, Olivier Jeanne, Pat Kehoe, Tim Kehoe,
Narayana Kocherlakota, Guido Lorenzoni, Andy Neumeyer, Fabrizio Perri, Victor Rios-Rull, Tom
Sargent, Stephanie Schmitt-Grohe, Martin Uribe, Mark Wright, and Jing Zhang for helpful comments
and suggestions. We also acknowledge valuable comments by participants at various seminars and
conferences since 2007. The views expressed herein are those of the authors and do not necessarily
reflect the views of the National Bureau of Economic Research.
© 2011 by Enrique G. Mendoza and Vivian Z. Yue. All rights reserved. Short sections of text, not
to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including
© notice, is given to the source.
A General Equilibrium Model of Sovereign Default and Business Cycles
Enrique G. Mendoza and Vivian Z. Yue
NBER Working Paper No. 17151
June 2011
JEL No. E32,E44,F32,F34
ABSTRACT
Emerging markets business cycle models treat default risk as part of an exogenous interest rate on
working capital, while sovereign default models treat income fluctuations as an exogenous endowment
process with ad-hoc default costs. We propose instead a general equilibrium model of both sovereign
default and business cycles. In the model, some imported inputs require working capital financing;
default triggers an efficiency loss as these inputs are replaced by imperfect substitutes; and default
on public and private obligations occurs simultaneously. The model explains several features of cyclical
dynamics around defaults, countercyclical spreads, high debt ratios, and key business cycle moments.
Enrique G. Mendoza
Department of Economics
University of Maryland
College Park, MD 20742
and NBER
mendozae@econ.umd.edu
Vivian Z. Yue
Department of Economics
19 West 4th Street
New York University
New York, NY 10012
zy3@nyu.edu
1
Introduction
Episodes of sovereign default are characterized by a striking set of empirical regularities. In
particular, the event windows plotted in Figure 1 for a cross-country sample of 23 default events
in the 1977-2009 period highlight the following three facts:
(1) Default events are associated with deep recessions. On average, GDP and consumption
fall about 5 percent below trend, and imported inputs and total intermediate goods fall nearly
20 percent below trend. Labor falls to a level about 15 percent lower than in the three years
prior to the defaults. Net exports jump about 10 percentage points of GDP in the span of the
two quarters before and after default events. These observations are in line with the …ndings
of Levy-Yeyati and Panizza (2006) showing that default events coincide with large GDP drops
in an event analysis for 39 developing countries covering the 1970-2005 period. In addition,
Tomz and Wright (2007) studied defaults from 1820 to 2004 and found the maximum default
frequency when output is at least 7 percent below trend.
(2) Interest rates on sovereign debt peak at about the same time as output hits its through
and defaults occur, and they are negatively correlated with GDP. These two empirical regularities
are visually evident by comparing the output and interest rate plots in Figure 1. In addition,
Neumeyer and Perri (2005) and Uribe and Yue (2006) report cyclical correlations between GDP
and country interest rates ranging from zero to -0.8, with averages of -0.55 in Neumeyer and
Perri and -0.42 in Uribe and Yue.1
(3) External debt as a share of GDP is high on average, and higher when countries default.
The mean debt ratio before the default events in Figure 1 was about 50 percent, and reached
about 72 percent at the time of the defaults. Looking at all emerging and developing countries, as
de…ned in IMF (2006), foreign debt was 1/3 of GDP on average over 1998-2005. Highly indebted
poor countries had the highest average debt ratio, at about 100 percent of GDP, followed by
the Eastern European and Western Hemisphere countries, with averages of about 50 and 40
percent of GDP respectively. Looking at defaults historically, Reinhart et al. (2003) report that
the external debt ratio averaged 71 percent of GDP for all developing country defaults in the
1824-1999 period. This is very close to the 72 percent mean estimate for our default events in
Figure 1.
1
Neumeyer and Perri used data for Argentina, Brazil, Korea, Mexico and the Philippines. Uribe and Yue
added Ecuador, Peru and South Africa, but excluded Korea.
1
0 4 8 12
quarter
e. Intermediate Goods
-20
-40
-3 -2 -1
0 1 2
year
g. Interest Rate
3
percent deviation
percent deviation
15
10
5
0
-5
-12 -8 -4
0
10
0
-10
-12 -8 -4
0 4 8 12
quarter
d. Imported Intermediate Goods
20
0
-20
-40
-3 -2 -1
0 1
year
f. Labor
2
3
0 1 2
year
h. Debt/GDP
3
1
0.8
-3 -2 -1
100
40
percent
percentage point
percent deviation
0 4 8 12
quarter
c. Trade Balance/GDP
b. Consumption
indexed to t-4=1
5
0
-5
-10
-12 -8 -4
percent deviation
percent deviation
a. GDP
20
0
-12 -8 -4
0 4
quarter
Median
8 12
50
-3 -2 -1
Mean
0 1
year
2
3
One Std. Error Band
Figure 1: Macroeconomic Dynamics around Sovereign Default Events
Note: GDP, consumption, and trade balance/GDP are H-P detrended. Imported inputs and
intermediate goods are log-linearly detrended. Labor data is indexed so that employment 4 years
before default equals 1.The event window for GDP is based on data for 23 default events over
the 1977- 2009 period. Due to data limitations, the sample period and/or the number of events
varies in some of the other windows. Full details are provided in the Data Appendix.
2
It has proven di¢ cult to provide a joint explanation of these stylized facts in International
Macroeconomics, because of a crucial disconnect between two key bodies of theory: On one hand,
quantitative models of business cycles in emerging economies explain countercyclical country interest rates by modeling the interest rate on sovereign debt as an exogenous interest rate charged
on foreign working capital loans obtained by …rms.2 In these models, default is exogenous and
hence facts (1) and (3) are left unexplained. On the other hand, quantitative models of sovereign default based on the classic setup of Eaton and Gersovitz (1981) generate countercyclical
sovereign spreads by assuming that a sovereign borrower faces shocks to an exogenous output
endowment with ad-hoc output costs of default.3 Since output is an exogenous endowment, these
models cannot address fact (1) and they do poorly at explaining fact (3). In short, business cycle
models of emerging economies cannot explain the default risk premia that drive their …ndings,
and sovereign default models cannot explain the cyclical output dynamics that are critical for
their results.
This paper proposes an equilibrium model of sovereign default and economic ‡uctuations
that provides a solution to the disconnect between those two classes of models. The model
features a transmission mechanism that links endogenous default risk with private economic
activity via the …nancing cost of working capital used to pay for a subset of imported inputs.
These subset of imported inputs can be replaced with other imported inputs or with domestic
inputs, but these are only imperfect substitutes, and as a result default causes an endogenous
e¢ ciency loss in production of …nal goods.
The contribution of this framework is that it is the …rst to provide a setup in which the
equilibrium dynamics of output and sovereign default are determined jointly, and in‡uence each
other via the interaction between foreign lenders, the domestic sovereign borrower, domestic
…rms, and households. In particular, a fall in productivity increases the likelihood of default
and hence sovereign spreads, and this in turn increases the …rms’ …nancing costs causing an
e¢ ciency loss that ampli…es the negative e¤ects of productivity shocks on output. This in turn
feeds back into default incentives and sovereign spreads.
Quantitative analysis shows that the model does well at explaining the three key stylized
facts of sovereign defaults. Moreover, the model’s …nancial ampli…cation mechanism ampli…es
the e¤ect of TFP shocks on output by a factor of 2.7 when the economy defaults, and the
model matches salient features of emerging markets business cycles such as the high variability
of consumption, the countercyclical dynamics of net exports, and the correlation between output
and default.
These results hinge on three important features of the model: First, the assumption that
producers of …nal goods require working capital …nancing to pay for imports of a subset of
intermediate goods. Second, the e¢ ciency loss in …nal goods production that occurs when the
country defaults, because the loss of access to credit for some imported inputs forces …rms to
2
3
See Neumeyer and Perri (2005), Uribe and Yue (2006) and Oviedo (2005).
See, for example, Aguiar and Gopinath (2006), Arellano (2008), Bai and Zhang (2005) and Yue (2010).
3
substitute into other imported and domestic inputs that are imperfect substitutes. Third, the
assumption that the government can divert the private …rms’repayment when it defaults on its
own debt.
The above key features of the model are in line with existing empirical evidence. Amiti
and Kronings (2007) and Halpern, Koren and Szeidl (2008) provide …rm-level evidence of the
imperfect substitutability between foreign and domestic inputs, and the associated TFP e¤ect of
changes in relative factor costs. In particular, they study the impact of reducing imported input
tari¤s on …rm-level productivity using data for Indonesia and Hungary, and …nd that imperfect
substitution of inputs accounts for the majority of the e¤ect of tari¤ cuts on TFP. Gopinath and
Neiman (2010) …nd important evidence of within-…rm shifts from imported to domestic inputs
in the Argentine debt crisis of 2001-2002. Reinhart and Rogo¤ (2010) and Reinhart (2010)
show that there is a tight connection between banking crises, with widespread defaults in the
non…nancial private sector, and sovereign defaults, and that private debts become public debt
after sovereign defaults.
The model’s …nancial transmission mechanism operates as follows: Final goods producers use
labor and an Armington aggregator of imported and domestic inputs as factors of production,
with the two inputs as imperfect substitutes. Domestic inputs require labor to be produced.
Imported inputs come in di¤erent varieties described by a Dixit-Stiglitz aggregator, and a subset
of them needs to be paid in advance using foreign working capital loans. Under these assumptions, the optimal input mix depends on the country interest rate (inclusive of default risk),
which is also the …nancing cost of working capital, and on TFP. When the country has access
to world …nancial markets, …nal goods producers use a mix of all varieties of imported inputs
and domestic inputs, and ‡uctuations in default risk a¤ect the cost of working capital and thus
induce “regular” ‡uctuations in factor demands and output. In contrast, when the country
defaults, …nal goods producers substitute away from the imported inputs that require working
capital …nancing, because of the surge in their …nancing cost. This reduces production e¢ ciency
sharply because of the imperfect substitutability across varieties of imported inputs and across
domestic and foreign inputs, and because in order to increase the supply of domestic inputs
labor reallocates away from …nal goods production.4
When the economy defaults, both the government and …rms are excluded from world credit
markets for some time, with an exogenous probability of re-entry as is common in quantitative
studies of sovereign default. Since the probability of default depends on whether the sovereign’s
value of default is higher than that of repayment, there is endogenous feedback between the
economic ‡uctuations induced by changes in default probabilities and country risk premia. In
particular, rising country risk in the periods leading to a default causes a decline in economic
4
As a result, part of the output drop that occurs when the economy defaults shows as a fall in the Solow
residual (i.e. the fraction of aggregate GDP not accounted for by capital and labor). This is consistent with the
data from emerging markets crises showing that a large fraction of the observed output collapse is attributed to
the Solow residual (Meza and Quintin (2006), Mendoza (2010)). Moreover, Benjamin and Meza (2007) show that
in Korea’s 1997 crisis, the productivity drop followed in part from a sectoral reallocation of labor.
4
activity as the …rms’…nancing costs increase. In turn, the expectation of lower output at higher
levels of country risk alters repayment incentives for the sovereign, a¤ecting the equilibrium
determination of default risk premia.
A key feature of our model is that the e¢ ciency loss caused by sovereign default generates an
endogenous output cost that is an increasing, convex function of TFP. This di¤ers sharply from
the two approaches followed to model ad-hoc costs of default in the literature. One approach
models default costs as a …xed percentage of the realization of an exogenous endowment when
a country defaults (e.g. Aguiar and Gopinath (2006), Yue (2010)). In this case, default is just
as costly, in percentage terms, in a low-endowment state as in a high-endowment state (i.e. the
percent cost is independent of the endowment realization), and hence average debt ratios are
low when the models are calibrated to actual default frequencies. The second approach is the
asymmetric formulation proposed by Arellano (2008). Below a certain threshold endowment
level, there is no cost of default, and above it the sovereign’s income is reduced to the same
constant level regardless of the endowment realization. Thus, in the latter case the percent cost
of default increases linearly with the endowment realization. This formulation makes default
more costly in good states, making default more likely in bad states and increasing debt ratios.
However, debt ratios in calibrated models are still much lower than in the data, unless features
like multiple maturities, dynamic renegotiation or political uncertainty are added.5
The default cost in our model is a general equilibrium outcome driven by the e¤ects of
sovereign risk on private markets. This endogenous cost adds “state contingency”to the default
option, allowing the model to support higher mean debt ratios at observed default frequencies.
Our baseline calibration supports a mean debt-output ratio of 23 percent, nearly four times
larger than in Arellano (2008). In addition, in our model outputs costs of default are always
incurred at equilibrium, whereas with Arellano’s formulation defaults occur mostly when the
endowment is lower than the threshold endowment value, so actual costs of default are zero
at equilibrium. Moreover, in our setup, output itself falls sharply when the economy defaults,
because the model’s …nancial transmission mechanism ampli…es the e¤ects of TFP shocks on
output. In contrast, in existing sovereign default models, large output drops can only result
form large, exogenous endowment shocks.
The assumptions that both foreign and domestic inputs and the varieties of imported inputs
are imperfect substitutes are critical for the above properties of the default cost.6 The cost
5
Arellano (2008) obtained a mean debt-output ratio of 6 percent using her asymmetric cost. Aguiar and
Gopinath (2006) obtained a mean debt ratio of 19 percent using the …xed percent cost, but at a default frequency
of only 0.23 percent. Yue (2010) used the same cost in a model with renegotiation calibrated to observed default
frequencies, and obtained a mean debt ratio of 9.7 percent. Studies that have obtained higher debt ratios with
modi…cations of the Eaton-Gersovitz environment, but still assuming exogenous endowments, include: Cuadra
and Sapriza (2008), D’Erasmo (2008), Bi (2008a) and (2008b), Chatterjee and Eyigungor (2008), Benjamin and
Wright (2008), and Lizarazo (2005).
6
If the inputs are perfect substitutes there is no output cost of default, because …rms can shift inputs without
a¤ecting production and costs. If they are complements, production is either zero (with unitary elasticity of
substitution) or not de…ned (with less-than-unitary elasticity) when the economy defaults and cannot access
imported inputs.
5
is higher and becomes a steeper function of TFP at lower elasticities of substitution, because
the inputs become less similar. The elasticity of labor supply also in‡uences the output cost
of default. In particular, the cost is larger the higher this elasticity, because default triggers a
reduction in total labor usage. However, output costs of default, and the e¢ ciency loss that
drives them, are still present even if labor is inelastic. Final goods producers still have to shift
from a subset of imported input varieties to other imported inputs and to domestic inputs, and
labor still reallocates from …nal goods to intermediate goods production.
The treatment of the …nancing cost of working capital in this paper di¤ers from the treatment
in Neumeyer and Perri (2005) and Uribe and Yue (2006), who treat this cost as an exogenous
variable calibrated to match the interest rate on sovereign debt. In contrast, in our setup both
interest rates are driven by endogenous sovereign risk. In addition, in the Neumeyer-Perri and
Uribe-Yue models, working capital loans pay the wages bill in full, while in our model …rms use
working capital to pay only for a subset of imported intermediate goods. This lower working
capital requirement is desirable because empirical estimates suggest that working capital is a
small fraction of GDP (Schmitt-Grohe and Uribe (2007) estimate 9.3 percent annually for the
United States, we estimate 6 percent for Argentina in Section 4).
Our analysis is also related to the literature documenting explicit and implicit sanctions on
trade ‡ows and trade credit in response to sovereign defaults. Both are relevant for our analysis
because the implications of our model are identical whether default triggers exclusion from
trade credit or trade sanctions a¤ecting imports of some intermediate goods. Kaletsky (1985)
argued that exclusion from trade credit might be the heaviest penalty that a defaulter faces. He
documented the exclusion from trade credit experienced by the countries that defaulted in the
1980s, and showed estimates of short-term private credit nearly as large as unpaid interest in
medium-term sovereign debt. More recently, Kohlscheen and O’Connell (2008) showed evidence
of sharp declines in trade credit from commercial banks during default episodes. Rose (2005)
conducted a cross-country analysis of trade ‡ows and default, and found that default has a large,
persistent negative e¤ect on bilateral trade between creditor and debtor countries, and Martinez
and Sandleris (2008) provided further empirical evidence on the association between sovereign
defaults and the decline in trade.
The rest of the paper proceeds as follows: Section 2 presents the model. Section 3 examines
the e¤ects of interest rate changes on production and factor allocations in partial equilibrium.
Section 4 explores the full model’s quantitative implications. Section 5 concludes.
2
A Model of Sovereign Default and Business Cycles
There are four groups of agents in the model, three in the “domestic” small open economy
(households, …rms, and the sovereign government) and one abroad (foreign lenders). There are
also two production sectors in the domestic economy, a sector f of …nal goods producers and a
6
sector m of intermediate goods producers.
2.1
Households
Households choose consumption and labor supply so as to maximize a standard time-separable
P1 t
u (ct g(Lt )) ; where 0 <
< 1 is the discount factor, and ct
utility function E
t=0
and Lt denote consumption and labor supplied in period t respectively. u( ) is the period
utility function, which is continuous, strictly increasing, strictly concave, and satis…es the Inada
conditions. Following Greenwood, Hercowitz and Hu¤man (1988), we remove the wealth e¤ect
on labor supply by specifying period utility as a function of consumption net of the disutility of
labor g(Lt ), where g( ) is increasing, continuously di¤erentiable and convex. This formulation
of preferences plays an important role in allowing international real business cycle models to
explain observed business cycle facts, and it also simpli…es the “supply side” of the model.7
Households take as given the wage rate wt , pro…ts paid by …rms in the f and m sectors
f
t;
m
t
and government transfers (Tt ). Households do not borrow directly from abroad, but
the government borrows, pays transfers, and makes default decisions internalizing their utility.8
Consequently, the households’optimization problem reduces to:
max E
ct ;Lt
s:t:
hX
t
u (ct
ct = wt Lt +
f
t
i
g (Lt )) ;
+
m
t
(1)
+ Tt :
(2)
The optimality condition for labor supply is:
g 0 (Lt ) = wt :
(3)
For purposes of the quantitative analysis, we de…ne g(L) =
elasticity of labor supply is given by 1=(!
with ! > 1: Hence, the Frisch
1). The period utility function takes the standard
constant-relative-risk-aversion form u (c; L) =
2.2
L!
!
(c L! =!)1
1
1
with
> 0.
Final Goods Producers
Firms in the f sector produce using labor Lft and intermediate goods Mt , and a time-invariant
capital stock k.9 They face Markov TFP shocks "t with a transition probability distribution
7
Removing the wealth e¤ect on labor supply is useful because otherwise the wealth e¤ect pushes labor to display
a counterfactual rise when TFP falls or when consumption drops sharply, as is the case in default episodes.
8
This assumption is very common in the Eaton-Gersovitz class of models but it is not innocuous, because
whether private foreign debt contracts are allowed, and whether they are enforceable vis-a-vis government external
debt, a¤ects the e¢ ciency of the credit market equilibrium (see Wright (2006)).
9
Sovereign debt models generally abstract from capital accumulation for simplicity. Adding capital makes the
recursive contract with default option signi…cantly harder to solve because it adds an additional endogenous state
variable. Moreover, changes in the capital stock have been estimated to play a small role in output dynamics
around …nancial crises (see Meza and Quintin (2006) and Mendoza (2007)).
7
function
("t j"t
1 ).
The production function is Cobb-Douglas:
yt = "t M mdt ; mt
with 0 <
L;
M;
k
< 1 and
+
L
M
+
M
(Lft )
L
k
(4)
k
= 1.
k
The mix of intermediate goods is determined by a standard CES Armington aggregator
that combines domestic inputs mdt and imported inputs mt , with the latter represented by a
Dixit-Stiglitz aggregator that combines a continuum of di¤erentiated imported inputs mj for
j 2 [0; 1]:
Mt =
h
mdt
+ (1
) (mt )
i1
;
"Z
mt
j2[0;1]
mjt
dj
#1=
(5)
The …rms’purchases of variety j of imported inputs are denoted by mjt . The “within”elasticity
of substitution across all varieties is given by
substitution between mt and
of domestic
and 0
inputs.10
< 1.
mdt
is de…ned as
mj
md ;m
= j1=(v
= j1=(
1)j. The Armington elasticity of
1)j and
is the Armington weight
The following parameter restrictions are assumed to hold: 0 <
;
<1
< 1 is necessary because without use of imported inputs default would be
costless. In addition, foreign and domestic inputs and the varieties of imported inputs need to
be imperfect substitutes (i.e. 0 < ;
< 1) in order for the output cost of default to increase
with "; as we show later.
Imported inputs are sold in world markets at exogenous time-invariant prices pj for j 2 [0; 1]
de…ned in terms of the price of …nal goods, which is the numeraire. The relative price of domestic
inputs pm
is an endogenous equilibrium price.
t
A subset
of the imported input varieties de…ned by the interval [0; ] ; for 0 <
to be paid in advance using working capital
…nancing.11
< 1, needs
The rationale for splitting imported
inputs this way is to provide for a ‡exible treatment of imported inputs, so that in default
episodes, when access to the set
of imported inputs is hampered by exclusion from credit
markets, imported inputs do not vanish, even though they adjust sharply, as observed in the
data.
We model working capital following the classic pay-in-advance setup of Fuerst (1992) and
Christiano and Eichenbaum (1992), which is also widely used in business cycle models of emerging economies (e.g. Neumeyer and Perri (2005), Uribe and Yue (2006), Mendoza (2010)). Working capital loans
t
are intraperiod loans repaid at the end of the period that are obtained from
10
This structure of aggregation of imported and domestic inputs is similar to those used in the empirical work
of Gopinath and Neiman (2010) and Halpern, Koren and Szeidl (2009).
11
We assume that the entire cost of purchasing the varieties in
needs to be paid in advance. Hence,
determines the "intensitity" of the working capital friction in a similar way as the standard working capital
models use to de…ne the fraction of the cost of a single input that is paid in advance (e.g. Neumeyer and
Perri (2005) and Uribe and Yue (2006). We could also introduce an extra parameter so that the varieties in
require that only a fraction of their cost be paid in advance, but lowering this fraction would have similar e¤ects
as keeping the fraction at 100 percent and lowering instead.
8
foreign creditors at the interest rate rt . This interest rate is linked to the sovereign interest rate
at equilibrium, as shown in the next section.
In our model, the standard pay-in-advance condition driving the demand for working capital
is:
t
1 + rt
Z
pj mj dj:
0
Pro…t-maximizing producers of …nal goods choose
t
(6)
so that this condition holds with equality.
Domestic inputs and the varieties of imported inputs in the [ ; 1] interval do not require working
capital, but this assumption is just for simplicity, the key element is that at high levels of country
risk (including periods without access to foreign credit markets) the …nancing cost of the set
of foreign inputs is higher than that of other inputs. Moreover, it is reasonable to assume that
trade in domestic inputs is largely intra-…rm trade and is at least partially collateralized by the
goods themselves, whereas this mechanism may not work as well for imported inputs because of
government interference with payments via con…scation or capital controls, which are common
during default episodes–as was clearly evident in Argentina’s 2001 default.
Final goods producers choose factor demands in order to maximize date-t pro…ts taking wt ,
rt , pj , and pm
t as given. Date-t Pro…ts are:
f
t
= "t (Mt )
M
Lft
L
k
k
Z
0
1
pj mjt dj
rt
Z
0
pj mjt dj
d
pm
t mt
wt Lft :
(7)
Following Uribe and Yue (2006), we show in Appendix 1 that the above static pro…t maximization problem follows from a standard problem maximizing the present value of dividends
subject to the working capital constraint. Moreover, Appendix 1 also establishes two features
of the …nal goods producers’optimal plans that are important for our model: First, the interest
rate determining the cost of working capital is the same as the between-period rate on one-period
loans. Second, since the …rms’ payo¤ function is linear and factor demands are characterized
by standard conditions equating marginal products to marginal costs (see below), …rms do not
have an incentive to build precautionary savings to self insure against changes in factor costs.
Furthermore, even if this incentive were at play, building up a stock of foreign deposits to provide
self-…nance of working capital to pay foreign suppliers is ruled out by the standard assumption of
the Eaton-Gersovitz setup that countries cannot build deposits abroad, otherwise debt exposed
to default risk cannot exist at equilibrium (as shown by Bulow and Rogo¤ (1989)).
R
1
The price of mt is the standard CES price index j2[0;1] pj
dj. Because some imported
inputs carry the …nancing cost of working capital, we can express this price index as follows:
P (rt ) =
Z
1
pj
As we show in the next Section, the set
1
dj +
Z
0
1
pj (1 + rt )
1
dj
:
of imported inputs is not used when a country defaults
9
because the …nancing cost becomes prohibitive (or equivalently, we could assume this is the case
because part of the punishment for default is exclusion from the
set of world input markets),
and hence when a country is in …nancial autarky the price index of imported inputs is:
P =
Z
1
1
pj
dj
1
when rt ! 1:
We use a standard two-stage budgeting approach to characterize the solution of the …nal
goods producers’ optimization problem. In the …rst stage, …rms choose Lft ; mdt and mt ; given
the factor prices wt ; pm
t and P (rt ), to maximize date-t pro…ts:
f
t
M
= "t M mdt ; mt
where M mdt ; mt =
mdt
L
Lft
k
d
pm
t mt
P (rt ) mt
k
wt Lft ;
(8)
1
+ (1
. Then, in the second stage they choose their
) (mt )
demand for each variety of imported inputs.
The …rst-order conditions of the …rst stage are:
M "t k
k
M
M mdt ; mt
M "t k
M
M mdt ; mt
k
L
Lft
(1
L
Lft
L "t k
k
) (mt )
Mt
M
1
mdt
Lft
1
L
1
= P (rt )
(9)
= pm
t
(10)
= wt :
(11)
Given mt , the second stage yields a standard CES system of demand functions for imported
inputs that can be split into a subset for varieties that do not require working capital and the
subset in
:
where P (rt ) =
R1
pj
1
mjt =
pj
P (rt )
mjt =
pj (1 + rt )
P (rt )
1
dj +
R
1
M ; for j 2 [ ; 1] ;
1
1
M ; for j 2 [0; ] :
1
0
pj (1 + rt )
1
dj
:
When the country is in default, and thus …nal goods producers cannot access working capital
…nancing, the demand function system becomes the limit of the above system as rt ! 1:
mjt =
P
pj
!
1
1
M ; for j 2 [ ; 1] ;
mjt = 0; for j 2 [0; ] ;
10
where P =
2.3
R1
1
1
pj
dj
.
Intermediate Goods Producers
Producers in the md sector use labor Lm
t and operate with a production function given by
A(Lm
t ) , with 0
1 and A > 0. A represents both the role of a …xed factor and an
invariant state of TFP in the md sector: Given pm
t and wt , the pro…t maximization problem of
intermediate goods …rms is:
m
t
max
m
Lt
m
= pm
t A(Lt )
wt Lm
t :
(12)
Their labor demand satis…es this standard optimality condition:
m
pm
t A(Lt )
2.4
1
= wt :
(13)
Equilibrium in Factor Markets and Production
Take as given a …nite interest rate rt , which means that sector f has access to credit markets,
and a TFP realization "t . The corresponding (partial) equilibrium factor allocations and prices
m
are given by the values of [mt ; mdt ; Lft ; Lm
t ; Lt ] and [pt ; wt ] that solve the following nonlinear
system:
M "t k
k
M
M mdt ; mt
M "t k
k
M mdt ; mt
L "t k
k
Lft
M
L
) (mt )
(1
Lft
M mdt ; mt
L
= P (rt )
(14)
= pm
t
(15)
= wt
(16)
= wt
(17)
g (Lt ) = wt
(18)
Lft + Lm
= Lt
t
(19)
1
mdt
M
1
L
Lft
m
pm
t A(Lt )
1
1
0
A(Lm
t )
= mdt
(20)
Conditions (14)-(20) drive the e¤ects of ‡uctuations in TFP and interest rates on production
and factor allocations. We study these e¤ects in detail in Section 3. Note also that during periods
of exclusion from world credit markets, the factor allocations and prices are determined as the
limiting case of the above nonlinear system as r ! 1. The sector f does not have access to
foreign working capital …nancing and hence to the set
of imported inputs.
Using the above optimality conditions, it follows that total value added valued at equilibrium
11
relative prices is given by (1
M )"t (Mt )
M
(Lft )
L
k
k
m
+ pm
t A(Lt ) . Moreover, given the CES
formulation of Mt , the value of imported inputs satis…es P (rt )mt =
d
pm
t mt
M "t (Mt )
M
(Lft )
L
k
k
. Given these results, we can calculate GDP as gross production of …nal goods minus
the cost of imported inputs, adjusting for the fact that in most emerging economies GDP at
constant prices is computed …xing prices as of a base year using Laspeyres indexes (while in the
model P (rt ) varies over time because of ‡uctuations in the rate of interest). Hence we de…ne
GDP as gdpt
2.5
yt
P mt , using a time-invariant price index of imported inputs.12
The Sovereign Government
The sovereign government trades with foreign lenders one-period, zero-coupon discount bonds,
so markets of contingent claims are incomplete. The face value of these bonds speci…es the
amount to be repaid next period, bt+1 . When the country purchases bonds bt+1 > 0, and when
it borrows bt+1 < 0. The set of bond face values is B = [bmin ; bmax ]
We set the lower bound bmin >
y
r,
R, where bmin
0
bmax .
which is the largest debt that the country could repay with
full commitment. The upper bound bmax is the highest level of assets that the country may
accumulate.13
The sovereign cannot commit to repay its debt. As in the Eaton-Gersovitz model, when the
country defaults it does not repay at date t and the punishment is exclusion from the world
credit market in the same period. The country re-enters the credit market with an exogenous
probability , and when it does it starts with a fresh record and zero debt.14
We add to the Eaton-Gersovitz setup an explicit link between default risk and private …nancing costs. This is done by assuming that a defaulting sovereign can divert the repayment of the
…rms’working capital loans to foreign lenders.15 Hence, both …rms and government default together. As explained in the introduction, this is in line with the historical evidence documented
by Reinhart and Rogo¤ (2010) and Reinhart (2010). We also provide empirical evidence later
in this Section showing a tight link between private and public borrowing costs.
The sovereign government chooses a debt policy (amounts and default or repayment) along
with private consumption and factor allocations so as to solve a recursive social planner’s problem.16 The state variables are the bond position and TFP, denoted by the pair (bt ; "t ), and the
12
We use P = 1, which follows from the fact that pj = 1 for all j 2 [0:1] and assuming a zero real interest rate
in the base year. Note, however, that changes in our quantitative results are negligible if we use the equilibirum
price index P (rt ) instead, because default is a low frequency event, and outside default episodes interest rates
display very small ‡uctuations.
13
bmax exists when the interest rates on a country’s saving are su¢ ciently small compared to the discount factor,
which is satis…ed in our paper since (1 + r ) < 1.
14
We asbtract from debt renegotiation. See Yue (2010), Bi (2008b) and Benjamin and Wright (2008) for
quantitative studies of sovereign default with renegotiation.
15
Notice that existing models of emerging markets business cycles with working capital (e.g. Neumeyer and
Perri (2005) and Uribe and Yue (2006)) already assume that the sovereign interest rates and priviate …nancing
costs are equal. Here we endogenize interest rates and the two rates are equalized as an equilibrium outcome.
16
We show in Appendix 2 that this planner’s problem yields the same equilibrium as a decentralized Ramseylike equilibrium in which the government maximizes households’ utility subject to the resource constraints, the
12
planner takes as given the bond pricing function qt (bt+1 ; "t ). Since at equilibrium the default
risk premium on sovereign debt will be the same as on working capital loans, the net interest
rate on working capital satis…es rt = 1=qt (bt+1 ; "t )
1. The planner’s payo¤ is given by:
n
o
V (bt ; "t ) = max v nd (bt ; "t ) ; v d ("t ) ;
(21)
where v nd (bt ; "t ) is the value of continuing in the credit relationship with foreign lenders (i.e.,
“no default”), and v d ("t ) is the value of default. If bt
0, the value function is simply v nd (bt ; "t )
because in this case the economy uses the credit market to save, receiving a return equal to the
world’s risk free rate r .
The continuation value is given by the choice of [ct ; mdt ; mt ; Lft ; Lm
t ; Lt ; bt+1 ] that solves this
constrained maximization problem:
v
nd
(bt ; "t ) =
max
ct ;mdt ;mt ;Lft ;Lm
t ;Lt ;bt+1
(
u (ct
g(Lt ))
+ E [V (bt+1 ; "t+1 )]
)
;
(22)
subject to:
ct + qt (bt+1 ; "t ) bt+1
bt
"t f M mdt ; mt ; Lft ; k
mt P
1
qt (bt+1 ; "t )
1 ;
(23)
Lft + Lm
t = Lt
d
A(Lm
t ) = mt
where f ( ) = M
M
(Lft )
L
k k : The …rst constraint is the resource constraint of the economy.
The last two constraints are the resource constraints in the markets for labor and domestic
inputs respectively.
Notice that the planner faces the same e¤ects of interest rates on output and factor allocations
operating via the working capital channel that a¤ects the private sector. In particular, for a given
bond pricing function qt (bt+1 ; "t ) and any pair (bt+1 ; bt ) 2 B, including the optimal choice of bt+1 ;
the optimal factor allocations chosen by the planner [mt ; mdt ; Lft ; Lm
t ; Lt ] satisfy the conditions
(14)-(20) that characterize equilibrium in factor markets, with wt and pm
t matching the shadow
prices given by the Lagrange multipliers of the resource constraints for labor and domestic
inputs. In addition, the planner internalizes the households’desire to smooth consumption, and
hence transfers to them an amount equal to the negative of the balance of trade (i.e. the ‡ow
of resources private agents need to …nance the gap between GDP and consumption).
government budget constraint, the constraint that factor allocations need to be consistent with private equilibrium
conditions, and the assumption that the diverted working capital repayments are not rebated to households (i.e.
they are an extra default cost or a tax used to …nance unproductive government purchases). We also discuss in
Appendix 2 the decentralized equilibrium in the alternative case in which these repayments are rebated.
13
d
The value of default is:
(
v ("t ) =
max
u (ct
g(L))
) Ev d ("t+1 ) +
+ (1
ct ;mdt ;mt ;Lft ;Lm
t ;Lt
EV (0; "t+1 )
)
;
(24)
subject to:
ct = "t f M mdt ; mt ; Lft ; k
mt P
(25)
Lft + Lm
t = Lt
d
A(Lm
t ) = mt
Note that v d ("t ) takes into account the fact that in case of default at date t; the country has
no access to …nancial markets that period, and hence the country consumes the total income
given by the resource constraint in the default scenario. In this case, since …rms cannot borrow
to …nance the subset
of imported inputs, the equilibrium allocations for [mdt ; mt ; Lft ; Lm
t ; Lt ]
and the price index P are those that solve system (14)-(20) as r ! 1. The value of default
at t also takes into account that at t + 1 the economy may re-enter world capital markets with
probability
1
and associated value V (0; "t+1 ), or remain in …nancial autarky with probability
and associated value v d ("t+1 ).
The de…nitions of the default set and the probability of default are standard from Eaton-
Gersovitz models (see Arellano (2008)). For a debt position bt < 0, default is optimal for the
set of realizations of "t for which v d ("t ) is at least as high as v nd (bt ; "t ):
n
D (bt ) = "t : v nd (bt ; "t )
o
v d ("t ) :
(26)
The probability of default at t + 1 perceived as of date t, pt (bt+1 ; "t ), can be induced from the
default set and the transition probability function of productivity shocks
pt (bt+1 ; "t ) =
Z
D(bt+1 )
d ("t+1 j"t ) :
("t+1 j"t ) as follows:
(27)
The economy is considered to be in …nancial autarky when it has been in default for at least
one period and remains without access to world credit markets. The optimization problem of
the sovereign is the same as the problem in the default period. This is the case because, since the
Bulow-Rogo¤ result requires the economy not to be able to access funds saved abroad during
periods of …nancial autarky, before defaulting the economy could not have built up a stock
of savings abroad to provide working capital …nancing to …rms to purchase imported inputs.
Alternatively, we can assume that the default punishment includes exclusion from both world
capital markets and the subset
of world markets of intermediate goods.
The model preserves these standard features of the Eaton-Gersovitz model: Given "t , the
value of defaulting is independent of the level of debt, while the value of not defaulting increases
14
with bt+1 , and consequently the default set and the equilibrium default probability grow with
the country’s debt. The following theorem formalizes these results:
Theorem 1 Given a productivity shock " and a pair of bond positions b0 < b1
is optimal for
satis…es p
b1 ,
b0 ; "
then default is also optimal for
p
b1 ; "
b0
0, if default
and the probability of default at equilibrium
.
Proof. See Appendix 3.
2.6
Foreign Lenders
International creditors are risk-neutral and have complete information. They invest in sovereign
bonds and in private working capital loans. Foreign lenders behave competitively and face an
opportunity cost of funds equal to r . Competition implies that they expect zero pro…ts at
equilibrium, and that the returns on sovereign debt and the world’s risk-free asset are fully
arbitraged:
qt (bt+1 ; "t ) =
(
1
1+r
[1 pt (bt+1 ;"t )]
1+r
if bt+1
0
if bt+1 < 0
:
(28)
This condition implies that at equilibrium bond prices depend on the risk of default. For a
high level of debt, the default probability is higher. Therefore, equilibrium bond prices decrease
with indebtedness. This result, formalized in Theorem 2 below, is again in line with the EatonGersovitz model and is also consistent with the empirical evidence documented by Edwards
(1984).
Theorem 2 Given a productivity shock " and bond positions b0 < b1
prices satisfy q
b0 ; "
0, the equilibrium bond
b1 ; " :
q
Proof. See Appendix 3.
The returns on sovereign bonds and working capital loans are also fully arbitraged. Because
the sovereign government diverts the repayment of working capital loans when it defaults, foreign
lenders assign the same risk of default to private working capital loans as to sovereign debt, and
hence the no-arbitrage condition between sovereign lending and working capital loans implies:
rt (bt+1 ; "t ) =
1
qt (bt+1 ; "t )
1, if
t
> 0:
(29)
This arbitrage result raises a key empirical question: Are the interest rates faced by sovereign
governments and private …rms closely related? Answering this question in full is beyond the
scope of this paper, but we do provide evidence suggesting that corporate and sovereign interest
rates tend to move together. To study this issue, we constructed estimates of …rm-level e¤ective
interest rates as the ratio of a …rm’s total debt service divided by its total debt obligations using
the Worldscope database. We then aggregated for each country by computing the median across
15
…rms. Table 1 reports these estimates of corporate interest rates together with the standard
EMBI+ measure of interest rates on sovereign debt, both as time-series averages over 1994 to
2005, as well as the correlations between the two over the same period.
Table 1 shows that the two interest rates are positively correlated in most countries, with a
median correlation of 0.7, and in some countries the relationship is very strong (see Figure 2).17
The Table also shows that, with the exceptions of Argentina, China and Russia, the e¤ective
…nancing cost of …rms is higher on average than the sovereign interest rates.
Table 1: Sovereign and Corporate Interest Rates
Country
Sovereign Interest Rates
Median Firm Interest Rates
Correlation
Argentina
13.32
10.66
0.87
Brazil
12.67
24.60
0.14
Chile
5.81
7.95
0.72
China
6.11
5.89
0.52
Colombia
9.48
19.27
0.86
Egypt
5.94
8.62
0.58
Malaysia
5.16
6.56
0.96
Mexico
9.40
11.84
0.74
Morocco
9.78
13.66
0.32
Pakistan
9.71
12.13
0.84
Peru
9.23
11.42
0.72
Philippines
8.78
9.27
0.34
Poland
7.10
24.27
0.62
Russia
15.69
11.86
-0.21
South Africa
5.34
15.19
0.68
Thailand
6.15
7.30
0.94
Turkey
9.80
29.26
0.88
Venezuela
14.05
19.64
0.16
There is also strong historical evidence in favor of the assumption driving the arbitrage of
private and government interest rates in the model, namely that the government diverts the
repayment of the …rms’ foreign obligations. This is documented in the comprehensive studies
by Reinhart and Rogo¤ (2010) and Reinhart (2010) and in Boughton’s (2001) historical account
of the IMF’s handling of the 1980s debt crisis (see in particular Chapter 9). These studies
show that it is common for governments to take over the foreign obligations of the corporate
sector in actual default episodes, particularly when a domestic banking crisis occurs in tandem
with sovereign default, which is a frequent occurrence. In addition, Arteta and Hale (2007)
17
Arellano and Kocherlakota (2007) and Agca and Celasun (2009) provide further empirical evidence of the
positive relationship between private domestic lending rates and sovereign spreads. Corsetti, Kuester, Meier and
Muller (2010) show that this feature is also present in the data of OECD countries.
16
and Kohlscheen and O’Connell (2008) provide evidence of signi…cant adverse e¤ects of sovereign
default on private access to foreign credit. Arteta and Hale show that there are strong negative
e¤ects on private corporate bond issuance during and after default episodes. Kohlscheen and
O’Connell document that the volume of trade credit provided by commercial banks falls sharply
when countries default. The median drops in trade credit are about 35 and 51 percent two and
four years after default events respectively.
Chile
Argentina
80
10
Interest Rate
Interest Rate
7
6
0
94 95 96 97 98 99 00 01 00
Year
4
99
Interest Rate
15
10
96
98
00
Year
00
01
02 03
Year
04
4
97 98 99 00 01 02 03 04 05
Year
05
Thailand
P eru
Mexico
20
8
6
5
02
04
12
14
11
12
10
10
Interest Rate
Interest Rate
40
20
Interest Rate
12
8
60
5
94
Malay sia
9
9
8
8
6
7
4
6
97 98 99 00 01 02 03 04 05
Year
2
97 98 99 00 01 02 03 04 05
Year
— — — Sovereign Bond Interest Rates - - - - Median Firm Financing Cost
Figure 2: Sovereign Bond Interest Rates and Median Firm Financing Costs
2.7
Recursive equilibrium
De…nition 1 The model’s recursive equilibrium is given by (i) a decision rule bt+1 (bt ; "t ) for
the sovereign government with associated value function V (bt ; "t ), consumption and transfers
rules c (bt ; "t ) and T (bt ; "t ) ; default set D (bt ) and default probabilities p (bt+1 ; "t ); and (ii) an
equilibrium pricing function for sovereign bonds q (bt+1 ; "t ) such that:
1. Given q (bt+1 ; "t ), the decision rule bt+1 (bt ; "t ) solves the social planner’s recursive maximization problem (21).
2. The consumption plan c (bt ; "t ) satis…es the resource constraint of the economy
3. The transfers policy T (bt ; "t ) satis…es the government budget constraint.
4. Given D (bt ) and p (bt+1 ; "t ) ; the bond pricing function q (bt+1 ; "t ) satis…es the arbitrage
condition of foreign lenders (28).
Condition 1 requires that the government’s default and borrowing decisions be optimal given
the interest rates on sovereign debt. Condition 2 requires that the private consumption and factor
17
allocations implied by these optimal borrowing and default choices be feasible.18 Condition 3
requires that the decision rule for government transfers shifts the appropriate amount of resources
between the government and the private sector (i.e. an amount equivalent to net exports when
the country has access to world credit markets, or zero when the economy is in …nancial autarky).
Notice also that given conditions 2 and 3, the consumption plan satis…es the households’budget
constraint. Finally, Condition 4 requires the equilibrium bond prices that determine country
risk premia to be consistent with optimal lender behavior.
A solution to the above recursive equilibrium includes solutions for sectoral factor allocations
and production with and without credit market access. A solution for equilibrium interest rates
on working capital as a function of bt+1 and "t follows from (29). Solutions for equilibrium
wages, pro…ts and the price of domestic inputs follow then from the …rms’optimality conditions
and the de…nitions of pro…ts described earlier.
3
Country Risk and Default Costs in Partial Equilibrium
3.1
Interest Rate Changes and Factor Allocations
The e¤ects of interest rate changes on factor allocations play a central role in our model because
they are a key determinant of both output dynamics and the output cost of default. We illustrate
these e¤ects by means of a partial-equilibrium numerical example in which the interest rate is
exogenous. We use the parameter values set in the calibration described in Section 4, and solve
for factor allocations and prices using conditions (14)-(20) for di¤erent values of r.
Figure 3 shows six charts with the allocations of L; Lf ; Lm ; M; md ; and m for values of r
ranging from 0 to 80 percent. Each chart includes results for the baseline calibration, in which
we set
=0.65, which corresponds to
md ;m
= 2:86, and
= 0:59; which implies
mj
=2.44.
In addition, we show four alternative scenarios in which all but one of the baseline parameter
values are changed. Two of the scenarios consider lower values of
threshold below which
md
md ;m
(1.96, which is the
and m switch from gross substitutes to gross complements, and
the Cobb-Douglas case of unitary elasticity).19 The other two scenarios assume a high within
elasticity of substitution across imported input varieties (
mj
=10) and inelastic labor supply.
To facilitate comparisons across these scenarios, the results are plotted as ratios relative to the
allocations when r = 0:
The charts in Figure 3 illustrate three e¤ects by which the rate of interest a¤ects equilibrium
factor allocations. First, as chart 3b shows, an increase in r reduces the aggregate demand for
m because of the direct e¤ect by which the hike in r increases the marginal cost of the subset
of
of imported inputs, which is in turn re‡ected in an increase in P (r). This is the case for
18
In addition, since factor allocations satisfy conditions (14)-(20), these allocations are also consistent with a
competitive equilibrium in factor markets.
19
Note that the threshold would be at the unitary elasticity of substitution if labor supply were inelastic.
18
any 0 <
< 1. Second, an increase in r has indirect e¤ects that lower the demand for total
intermediate goods (M ) and labor in the …nal goods sector (Lf ), because of the Cobb-Douglas
structure of the production function of …nal goods (see charts 3a and 3e). The direction of these
e¤ects is also the same for any 0 <
< 1. Third, an increase in r has e¤ects on the output
and labor allocations in the intermediate goods sector, but the direction of these do depend on
the value of
in
md
and
(within the (0; 1) range). In particular, higher r leads to an increase or a decline
Lm
depending on whether the value of
makes imported and domestic inputs gross
substitutes or complements (see charts 3c and 3f). If
to be gross substitutes (complements), both
md
and
Lm
md
and
is high (low) enough for the two inputs
Lm
increase (fall) as r and Pm (r) rise, so
rise (fall) as m falls. As a result, the decline in M and L produced by an increase
in the rate of interest is larger when domestic and foreign inputs are gross complements than
when they are gross substitutes (see charts 3a and 3d).
a.Total intermediate goods (M)
1
b.Imported intermediate goods (m*)
1
c.Domestic intermediate goods (md)
1.02
0.9
0.95
1
0.8
0.7
0.9
0.98
0.6
0.85
0.8
0
0.96
0.5
0.4
0.2
0.4
0.6
0.8
0
d.Total labor (L)
0.2
0.4
0.6
0.8
e.Labor in f inal goods sector(Lf )
0.94
0
0.2
0.4
0.6
0.8
f .Labor in intermediate sector(Ld)
1
1
1.02
0.98
0.98
0.96
0.96
0.94
0.94
1
0.98
0.96
0.94
0.92
0.92
0
0.2
0.4
Baseline
0.6
0.8
0
0.92
0.2
0.4
Threshold Arming ton elasticity
0.6
Cobb-D oug las
0.8
0
Inelastic labor
0.2
0.4
0.6
0.8
Hig h within elasticity
Figure 3: E¤ects of interest rate shocks on intermediate goods and labor allocations
Compare now the baseline case with the inelastic labor scenario. The e¤ect on m is nearly
unchanged. M falls less with inelastic labor, however, because md rises more, and this is possible
19
because with inelastic labor supply L cannot fall in response to interest rate hikes, and this results
in a larger increase in Lm and a smaller decline in Lf . Thus, even with inelastic labor supply,
increases in r a¤ect the e¢ ciency of production by inducing a shift from foreign to domestic
inputs, and by reallocating a given total labor endowment from production of …nal goods to
production of intermediate goods.
Finally, compare the interest rate e¤ects of the baseline case with the scenario with high
within elasticity, in which
mj
= 10 (v = 0:9). As imported inputs become better substitutes,
the e¤ect of higher interest rates increasing the marginal cost of the
set of imported inputs
weakens, since imported inputs that do not require payment in advance are closer substitutes
of those that do. As a result, aggregate m falls less as the interest rate rises, causing a smaller
decline (rise) in M (md ), and less reallocation of labor from sector f to sector m.
Notice that qualitatively the e¤ects of increasing
md ;m
or
mj
are similar. The higher either
of these two elasticities are, the weaker the working capital channel, and hence the weaker the
e¤ects of interest rate ‡uctuations on production and factor allocations. The two are not equivalent, however, because when imported input varieties become better substitutes, …nal goods
producers can substitute into varieties outside the
set facing exogenous prices pj , whereas when
domestic inputs become better substitutes, substituting away into domestic inputs is done facing
an endogenous price pm . In our baseline calibration, we found that (again in the partial equilibrium setup used in Figure 3) changing
md ;m
allocations much more than changing
mj :
In particular, consider that in Figure 3, as we move
from the threshold Armington elasticity case (
are increasing
md ;m
alters the size of the interest rate e¤ects on factor
md ;m
= 1:96) to the baseline (
md ;m
= 2:86) we
by a factor of about 1.5, while moving from the baseline to the
scenario we are increasing
mj
mj
= 10
by a factor of 5, yet the amount by which interest rate e¤ects
di¤er from the baseline is similar in both cases. Moreover, we also computed scenarios with
values of
mj
lower than the baseline and obtained negligible changes in interest rate e¤ects
relative to the baseline.
3.2
Output costs of default
Using the same numerical example, we can now examine how the output cost of default varies
with "; and how this relationship depends on ; v and !. Figure 4 shows two plots of the output
cost of default as a function of ": The plot on the left compares the case with baseline parameters
with a scenario in which we lower
from the 0.65 baseline value to 0.4 (
md ;m
falls from 2:86
to 1:66). The plot on the right compares the baseline scenario with a scenario in which we lower
from 0.59 to 0.3 (
mj
falls from 2:43 to 1:43). For each value of " in the horizontal axis, the
output cost of default is measured as the percent fall in output that occurs when the government
defaults, which is computed as the value of output implied by the factor allocations that result
from conditions(14)-(20) as r ! 1 relative to the level implied by the same conditions when
r = 0:01.
20
Figure 4 illustrates three key properties of the model: First, the output cost of default
is increasing and convex in ". This is the case because, with Cobb-Douglas technologies and
competitive markets, the negative e¤ect of increases in marginal costs on factor demands is
larger at higher TFP levels.20 Second, the cost of default is higher the lower is
md ;m
. This is
an implication of the previous results showing that the negative e¤ects of interest rate shocks
on factor allocations are larger when domestic inputs are poorer substitutes of imported inputs.
Third, the cost of default is also higher the lower is
mj ,
although the e¤ect of varying
on the
output cost of default is considerably smaller than the e¤ect of varying , in line with what we
found earlier.
0.16
0.08
0.14
Baseline µ=0.65
µ=0.4
0.1
0.08
0.07
GDP cost
GDP cost
0.12
0.06
ν=0.3
0.05
0.06
0.04
0.04
0.03
-0.2 -0.1
0
0.1 0.2
log of TFP shock
Baseline ν=0.59
-0.2 -0.1
0
0.1 0.2
log of TFP shock
Figure 4: Output Costs of Default as a Function of TFP Shock
The fact that the output cost of default increases with " implies that default is more painful
at higher TFP levels. This result is critical for the model’s ability to support high debt levels
at the observed default frequencies, and producing defaults in “bad” times, because it makes
default more attractive at lower states of productivity. In this way, default works as a desirable
implicit hedging mechanism given the incompleteness of asset markets.
Figure 5 illustrates further how the cost of default declines as
md ;m
rises. This Figure plots
the output cost of default for a constant value of TFP (" = 1) at di¤erent values of
md ;m
.
Again, the cost of default becomes smaller at higher Armington elasticities because the inputs
are closer substitutes, and hence the e¢ ciency loss when …rms shift to use fewer foreign inputs
is smaller. Quantitatively, the Figure shows that already for
20
md ;m
> 4, the mechanism driving
This is the case in turn because of the "strong" convexity of Cobb-Douglas marginal products. Consider for
simplicity the case in which production "F (m) requires a single input m. In this case, “strong convexity” means
that F (m) satis…es F 000 (m) > (F 00 (m))2 =F 0 (m), which holds in the Cobb-Douglas case.
21
e¢ ciency losses in the model becomes very weak and is e¤ectively the same as if the inputs were
perfect substitutes.
Output costs of default for a neutral TFP shock at different
elasticities of substitution
Elasticity of substitution between foreign and domestic intermediate
20.00
4.00
2.86
1.96
1.00
percent GDP drop at default
0
-5
-10
-15
-20
-25
-30
Figure 5: Output Costs of Default at a Neutral TFP Shock
A similar analysis of the output costs of default as the one illustrated in Figures 4 and 5
but for di¤erent values of ! (instead of
and ) shows that a higher labor supply elasticity
(i.e. lower !) increases the cost of default, converging to about 11.5 percent for in…nitely elastic
labor supply. The output cost of default is increasing in TFP for any value of !, but, in contrast
with what we found for , the slope of the relationship does not change as ! changes.21
The labor market equilibrium illustrated in Figure 6 provides the intuition behind the result
that higher labor supply elasticity produces larger output costs of default. For simplicity, we
plot labor demands and supply as linear functions. The labor demand functions are given by the
marginal products in the left-hand-side of (11) and (13), and the labor supply is given by the
marginal disutility of labor in the left-hand-side of (3). Since labor is homogenous across sectors,
total labor demand is just the sum of sectoral demands. The initial labor market equilibrium is
at point A with wage w , total labor L and sectoral allocations Lm and Lf .
Consider now a positive interest rate shock. This leads to a reduction in labor demand in …nal
~ D . This occurs because, as explained earlier, higher r causes a reduction in
goods from LD to L
f
f
M and the marginal product of Lf is a negative function of M (since the production function is
e D .22 The new labor market
Cobb-Douglas). As a result, total labor demand shifts from LD to L
e The wage rate, the total labor allocation, and the labor allocated to
equilibrium is at point A.
21
We also found that adjusting A has qualitatively similar e¤ects as changing !.
In Figure 6, we hold constant pm for simplicity. At equilibrium, the relative price of domestic inputs changes,
and this alters the value of the marginal product of Ld, and hence labor demand by the m sector. The results
22
22
…nal goods are lower than before, while labor allocated to production of domestic inputs rises
(assuming that foreign and domestic inputs are gross substitutes). In contrast, assuming that
labor is in…nitely elastic would make Ls an horizontal line at the level of w and the interest
rate hike would leave w unchanged. As a result, L falls more, Lm is unchanged instead of rising,
and Lf falls less.23 Hence, the adverse e¤ect on output is stronger. At the other extreme, with
inelastic labor Ls is a vertical line at the level of L . Now L cannot change, but w falls more
than in Figure 6, Lm rises more, and Lf falls more. Hence, the decline in output is smaller.
w
S
L
w*
~
w
A
B
~
A
~
B
LD = LDf + LDm
~
Lf
LDm
~
~
L D = L Df + LDm
*
f
L
~
L*m Lm
~
L
L*
L, L f , Lm
Figure 6: Interest Rate Shocks and the Labor Market Equilibrium
4
4.1
Quantitative Analysis
Baseline Calibration
We study the quantitative implications of the model by conducting numerical simulations setting
the model to a quarterly frequency and using a baseline calibration based largely on data for
Argentina, as is standard practice in quantitative studies of sovereign default. Table 2 shows
the calibrated parameter values.
of our numerical analysis do take this into account and still are roughly in line with the intuition derived from
Figure 6.
23
D
The last e¤ect hinges on the fact that the gap between LD
widens as the wage falls. This is a property
m and L
of factor demands with Cobb-Douglas production.
23
Table 2: Baseline Calibration
Value Target statistics
Calibrated Parameters
Int. goods share in gross output of …nal goods
m
0.43
Argentina’s national accounts
Capital share in gross output of …nal goods
k
0.17
Standard capital share in GDP (0.3)
Labor share in gross output of …nal goods
L
0.40
Standard labor share in GDP (0.7)
Labor share in GDP of int. goods
0.7
Standard labor share in GDP (0.7)
Coe¢ cient of relative risk aversion
2
Standard RBC value
Risk-free interest rate
r
1%
Standard RBC value
Curvature parameter of labor supply
!
1.455
Frisch wage elasticity (2.2)
Re-entry probability
0.083
Dias and Richmond (2007)
Armington weight of domestic inputs
0.62
Regression estimate
Armington curvature parameter
0.65
Regression estimate
Dixit-Stiglitz curvature parameter
0.59
Gopinath and Neiman (2010)
Parameters set with SMM
Value
Autocorrelation of TFP shocks
"
Standard deviation of TFP shocks
A
Intermediate goods TFP coe¢ cient
Subjective discount factor
Upper bound of imported inputs
Targets from data
0.95
GDP autocorrelation
0.82
1.7%
GDP std. deviation
4.7%
0.31
Output drop in default
13%
0.88
Default frequency
0.69%
Working capital
0.7
with working capital
-0.67
TFP semi-elasticity of exogenous capital ‡ows
The share of intermediate goods in gross output
6%
to GDP ratio estimate
M
Net exports/GDP at default
10%
is set to 0.43, which corresponds to
the average ratio of intermediate goods to gross production calculated using annual data for
Argentina for the period 1993-2005 from the United Nation’s UNData.24 Given
k
= 0:17 so that the capital income share in value added of the f sector (
matches the standard 30 percent (0:17=(1
share in gross output of …nal goods of
value added of
L =(1
M)
L
M,
k =(1
we set
M ))
0:43) = 0:3). These factor shares imply a labor
=1
M
k
= 0:40, which yields a labor share in
= 0:7 in line with the standard 70 percent labor share. The labor
share in intermediate goods production
The risk aversion parameter
is also set to 0.7.
is set to 2 and the quarterly world risk-free interest rate r is
set to 1 percent, which are standard values in quantitative business cycle and sovereign default
studies. The curvature of labor disutility in the utility function is set to ! = 1:455, which implies
a Frisch wage elasticity of labor supply of 1=(!
1) = 2:2. This is the value typically used in
RBC models of the small open economy (e.g. Mendoza (1991) and Neumeyer and Perri (2005)),
and is based on estimates for the U.S. quoted by Greenwood, Hercowitz and Hu¤man (1988).
24
Mendoza (2010) reports a very similar share for Mexico, and Gopinath, Itskhoki, and Rigobon (2010) show
shares in the 40-45 percent range for several countries.
24
The probability of re-entry after default is 0.083, which implies that the country stays in
exclusion for three years after default on average. This is the estimate obtained by Dias and
Richmond (2007) for the median duration of exclusion using a partial access de…nition of reentry. A three-year exclusion period is also in the range of the estimates reported by Gelos et
al. (2003).25
The values of
and
are set using data on the ratio of imported to domestic intermediate
goods at constant prices and the associated relative prices, together with the condition equating
the marginal rate of technical substitution between m and md with the corresponding price
ratio (which follows from conditions (14) and (15)). National Accounts data for Argentina,
however, do not provide a breakdown of intermediate goods into domestic and imported, so
we obtained them instead from Mexican data for the period 1988-2004 and assumed that the
ratios are similar.26 A nonlinear regression of the optimality condition implied by (14) and (15)
produced estimates of
= 0:65 and
= 0:62, both statistically signi…cant (with standard errors
of 0.11 and 0.12 respectively). These two estimates also allow the model to match the average
ratios of imported to domestic inputs at current and constant prices in the Mexican data, which
are 18 and 15.7 percent respectively.
The values
= 0:65 and
= 0:62 imply that
md ;m
= 2:9 and that there is a small bias in
favor of domestic inputs. This Armington elasticity is in the range of existing empirical estimates
for several countries, but the estimates vary widely. McDaniel and Balistreri (2002) review the
literature and quote estimates ranging from 0.14 to 6.9. They explain that elasticities tend to be
higher when estimated with disaggregated data, in cross-sectional instead of time-series samples,
or when using long-run instead of short-run tests. In the next Section we conduct sensitivity
analysis to study the e¤ects of changing this and other key parameters on our main quantitative
…ndings.
The value of v is di¢ cult to set because it requires analysis of disaggregated data on imported intermediate goods. Gopinath and Neiman (2010) examined a large …rm-level dataset
for Argentina that included the disaggregation of import varieties. They focused in particular
on the dynamics of trade adjustment at the …rm level around the 2002 default event. We set
mj
= 2:44 (v = 0:59) in line with the elasticity across varieties that they reported. They also
concluded, in line with our argument, that trade adjustment via the extensive margin at the …rm
level, with …rms shifting from imported to domestic inputs, was very signi…cant in the aftermath
of Argentina’s default. Interestingly, they also set
25
md ;m
= 2:08 ( = 0:519), which is close to
The two studies use di¤erent de…nitions of re-entry. Gelos et al. use actual external bond issuance of public
debt. Dias and Richmond de…ne rentry when either the private or public sectors can borrow again, and they also
distinguish partial reaccess from full reaccess (with the latter de…ned as positive net debt ‡ows larger than 1.5
percent of GDP). Gelos et al. estimate an avearge exclusion of 5.4 years in the 1980s and nearly 1 year in the
1990s.
26
Several countries have input expenditure ratios similar to Mexico’s, but the ratios can vary widely. Goldberg
and Campa (2008) report ratios of imported inputs to total intermediate goods for 17 countries that vary from
14 to 49 percent, with a median of 23 percent. This implies ratios of imported to domestic inputs in the 16-94
percent range, with a median of 30 percent.
25
the value in our calibration.
Calibrating the model to the data also requires accounting for the fact that, contrary to what
the model predicts, international capital ‡ows, and the trade imbalances they …nance, do not
vanish completely when sovereigns default on private lenders–trade balances actually rise into
surpluses, as shown in Figure 1.27 An important component of these continuing capital ‡ows are
those vis-a-vis international organizations, on which countries very rarely default.28 In the case
of Argentina, the country made repayments to international organizations for about 2.7 percent
of GDP in 2002 and as large as 5 percent of GDP by 2006. To adjust our quantitative analysis
accordingly, we introduce an amount xt of exogenous capital ‡ows that are independent of the
borrowing and default decisions. For simplicity, and to prevent these capital ‡ows from altering
default incentives signi…cantly, we assume that xt is perfectly correlated with TFP and given
by xt = ln "t , and calibrate the semi-elasticity parameter
to data for Argentina as described
below. In addition, we will show later that the key features of our quantitative results, except
for surge in net exports during the exclusion period, are invariant to removing xt :
We calibrate the remaining six parameters (
2
",
,
A,
, , and ) using the simulated
method of moments (SMM) to target a set of moment conditions from the data. Productivity
shocks in …nal goods production follow an AR(1) process:
log "t =
with
iid
t
N 0;
2
" log "t 1
+ t;
(30)
. We use Tauchen’s (1986) quadrature method to construct a Markov
approximation to this process with 25 realizations. Data limitations prevent us from estimating
(30) directly using actual TFP data, so we set
2
and
"
in the SMM procedure to target
the standard deviation and …rst-order autocorrelation of quarterly H-P detrended GDP. We
use seasonally-adjusted quarterly real GDP from Argentina’s Ministry of Economy and Finance
(MECON) for the period 1980Q1 to 2005Q4. The standard deviation and autocorrelation of the
cyclical component of GDP are 4.7 percent and 0.79 respectively. The TFP process obtained
using SMM features
"
= 0.95 and
The targets for setting A,
;
= 1.7 percent.
and
are, respectively, the decline in output at default,
the frequency of default, the share of working capital …nancing in GDP, and the rise in the
trade balance-GDP ratio at default.29 The default frequency is 0.69 percent, since Argentina
27
The prediction that net exports go to zero when the country is excluded from credit markets is not particular
to our model. All existing quantitative models of sovereign default in the Eaton-Gersovitz class have the same
feature, because the only way to …nance a trade imbalance in this class of models is with foreign credit.
28
Only 23 countries have defaulted on the IMF since it was created in 1945 (see Aylward and Thorned (1998)),
and these are low income countries or countries in armed con‡icts without access to private lenders (e.g. Liberia,
Somalia, Congo, Sudan, Afghanistan, Iraq). In all the sovereign defaults included in the event analysis of Figure
1, payments to the IMF continued even after countries defaulted on private lenders, except in the case of Peru in
the 1980s.
29
A is useful for targeting the output drop at default because, as mentioned in Section 2, changes in A have
similar e¤ects as changes in !. In particular, lower values of A yield larger output drops at default without
altering the slope of the relationship between TFP and these output drops.
26
has defaulted …ve times since 1824 (the average default frequency is 2.78 percent annually or
0.69 percent quarterly). Output in the …rst quarter of 2002 was 13 percent below trend.30
The trade-balance output ratio rose by 10 percentage points in the quarter when Argentina
defaulted. Lacking working capital data, we follow Schmitt-Grohe and Uribe’s (2007) strategy
to proxy working capital as the fraction of M1 held by …rms, using an estimate for the U.S.
showing that …rms own about two-thirds of M1. Using Argentina’s M1 data and the same twothirds of …rm ownership, we estimate Argentina’s working capital at about 6 percent of GDP.
Given all these targets, the SMM procedure yields A = 0:31,
4.2
= 0:88 ,
= 0:7, and
=
0:67:31
Cyclical Co-movements in the Baseline Simulation
We evaluate the quantitative performance of the model by comparing moments from the data
with moments from the model’s stochastic stationary state. In order to compute the latter, we
feed the TFP process to the model and conduct 2000 simulations, each with 500 periods and
truncating the …rst 100 observations.
Table 3 compares the moments from Argentine data (Column (1)) with those produced by
the model (Column (2)). The data for National Accounts aggregates is from the sources noted in
the calibration. The debt data are from the World Bank’s GDF dataset for the 1980-2005 period.
The bond spreads data are quarterly EMBI+ spreads on Argentine foreign currency denominated
bonds from 1994Q2 to 2001Q4, taken from J.P. Morgan’s EMBI+ dataset. Labor is measured
using the employment rate from Argentina’s INDEC Permanent Survey of Households. These
data yield a similar correlation between labor and the country real interest rate as the one in
Neumeyer and Perri (2005) (-0.49 in our data v. -0.45 in their paper). Note also that in Table
3 we follow the sovereign default literature in listing data correlations relative to bond spreads,
rather than relative to country interest rates, as in Neumeyer and Perri, but the correlations
are similar using either variable (e.g. the correlation between GDP and the interest rate is -0.57
and with the spread is -0.62).
Table 3 shows that the model produces a debt-to-GDP ratio of almost 23 percent on average.
This is mainly the result of the e¤ects on default incentives of the large output drop that occurs
when the country defaults, and the increasing output cost of default as a function of TFP.
Although a 23 percent average debt ratio is still below Argentina’s 35 percent, it is much larger
than the mean debt ratios typically obtained in quantitative models of sovereign default with
exogenous output costs already targeted to improve the models’quantitative performance. For
30
Argentina declared default in the last week of December in 2001, but it is reasonable to assume that, in
quarterly data, the brunt of the real e¤ects of the debt crisis were felt in the …rst quarter of 2002. Arellano (2008)
also follows this convention to date the default as of the …rst quarter of 2002. She estimated the output cost at
14 percent, measured as a deviation from a linear trend.
31
Note that
is relatively low compared to typical RBC calibrations, but is in the range of values used in
sovereign default models (e.g.
in Aguiar and Gopinath (2006), Arellano (2008), and Yue (2010) ranges from
0:8 to 0:953). These lower discount factors are often justi…ed by arguing that political economy incentives lead
government decision-makers to display higher rates of time preference.
27
instance, Arellano (2008) obtained a mean debt ratio of 6 percent of GDP calibrating her
asymmetric cost of default so that income when the economy defaults is the maximum of the
actual endowment realization or 97 percent of the average endowment. Yue’s (2010) model with
renegotiation and an exogenous two-percent proportional output cost of default produced an
average debt ratio of 9.7 percent. Using the same default cost, Aguiar and Gopinath (2006)
obtained a higher mean debt ratio (27 percent), but with a default frequency of only 0.02
percent. In contrast, our baseline model produces a 23 percent debt ratio at the 0.7 percent
default frequency observed for Argentina.
Table 3: Statistical Moments in the Baseline Model and in the Data
(1)
(2)
(3)
Statistics
Data
Model
Model w/o xt
Average debt/GDP ratio
35%
22.89%
21.52%
Average bond spreads
1.86%
0.71%
1.02%
Std. dev. of bond spreads
0.78%
1.20%
1.43%
Consumption std. dev./GDP std. dev.
1.44
1.04
1.07
bond spreads
-0.62
-0.21
-0.25
trade balance
-0.87
-0.53
-0.32
labor1
0.39
0.52
0.53
0.90
0.99
0.99
trade balances
0.82
0.19
0.11
labor1
-0.42
-0.24
-0.34
-0.39
-0.23
-0.24
-0.112
-0.11
-0.11
61.5%2
86%
84%
32.0%2
37%
47%
Correlations with GDP
intermediate
goods1
Correlations with bond spreads
intermediate
goods1
Historical default-output co-movements
correlation between default and GDP1
fraction of defaults with GDP below
trend1
fraction of defaults with large recessions1
Note 1: Statistical moment computed at annual frequency.
Note 2: Cross-country historical estimate for 1820-2004 from Tomz and Wright (2007).
Large recessions in Tomz and Wright are deviations from trend in the range -11 to -7 percent,
and in the model are recessions with GDP at least two standard deviations below trend (i.e.
deviations from trend of at least -9.2 percent).
The variability of the spreads is higher in the model than in the data, while the mean spread
in the model is smaller than in the data. The mean spread of 0.71 percent in the model is close to
the default frequency, because we assume a zero recovery rate on defaulted debt and risk-neutral
creditors, which imply that bond spreads are linked one-to-one with default probabilities (see
28
eq. (28)). Thus, the model can only generate an average bond spread of a similar magnitude as
the default frequency.
The model yields a negative correlation between spreads and GDP, albeit less negative than
in the data, because sovereign bonds have higher default risk in bad states. As we noted
in the Introduction, both quantitative models of sovereign default and of business cycles in
emerging economies also produce countercyclical interest rates, but in the former output is
an exogenous endowment and in the latter country risk is exogenous. In contrast, our model
produces countercyclical country risk in a setting in which both output and country risk are
endogenous, and in‡uence each other.
The model is also consistent with two key stylized facts of emerging markets business cycles: countercyclical net exports and consumption variability that exceeds output variability
(although the model underestimates both moments relative to the data). The …rst result follows
from the fact that, when the country is in a bad TFP state, it faces higher interest rates and
tends to borrow less from abroad. The country’s trade balance thus increases, leading to a negative correlation between net exports and output. The second result occurs because the ability
to use external debt to smooth consumption is negatively a¤ected by the higher interest rates
induced by increased default probabilities. The sovereign borrows less when the economy faces
an adverse TFP shock, and thus households adjust consumption by more than in the absence
of default risk. On the other hand, because agents are impatient, the benevolent government
borrows more to increase private consumption when the TFP shock is good. Hence, the variability of consumption rises. As with the countercyclical spreads, existing models of sovereign
default and emerging markets business cycles can also account for countercyclical net exports
and consumption variability in excess of GDP variability, but working under the assumption
that either country risk or output ‡uctuations are exogenous.
The model predicts correlations of labor and intermediate goods with bond spreads and
with GDP in line with those observed in the data. The correlation of GDP with intermediate
goods is 0.90 in the data, compared with 0.99 in the model, and with spreads (before the 2002
default) is -0.39, compared with -0.23 in the model.32 The correlation of GDP with labor is
0.39 in the data v. 0.52 in the model, and with spreads is -0.42 v. -0.24 in the model. The
negative correlations of labor and intermediate goods with the interest rate are due to the credit
transmission mechanism that operates via working capital (as explained in Section 2). In turn,
intermediate goods and labor are positively correlated with GDP because of the standard realbusiness-cycle e¤ects of TFP shocks, and because of the reinforcing e¤ect of the countercyclical
spreads.
Interestingly, interest rate ‡uctuations and working capital have important e¤ects in our
model even though average sovereign spreads, and hence the average interest rate on working
32
We exclude …nancial autarky periods in computing correlations with spreads because in the model the default
spread goes to in…nity when the economy defaults, and hence correlations with the country interest rate are
unde…ned.
29
capital, do not di¤er much from the one-percent risk free rate. In contrast, Neumeyer and Perri
(2005) and Uribe and Yue (2006) found working capital to be important for emerging markets
business cycles using average interest rates around 7 percent and assuming that 100 percent of
the wages bill is paid with credit (i.e. the share of working capital in GDP is about 2/3rds).
Thus, as Oviedo (2005) also showed, in their models signi…cant e¤ects of working capital require
high interest rates on average and a large ratio of working capital credit, while our model requires
an average interest rate of about 1.7 percent and a working capital credit requirement calibrated
to an Argentine estimate of only 6 percent of GDP:
We also report in Table 3 three moments that pertain to the relationship between default
and output in historical cross-country data for the period 1820-2004 based on the work of Tomz
and Wright (2007): The correlation between defaults and GDP and the fractions of defaults
that occur when GDP is below trend and when recessions are unusually large. Because these
are moments based on annual data, we show comparable annual-equivalent moments from the
model. The correlation between defaults and GDP in the model is a close match to the actual
correlation. The model can produce defaults that occur in good times (de…ned as GDP above
trend) at the annual frequency, but this happens only with 14 percent of defaults. Hence, 86
percent of defaults occur with GDP below trend, which is roughly 25 percentage points more
than in the data. On the other hand, the model is close to the data in terms of the fraction of
defaults that occur with deep recessions. In the model, 37 percent of defaults occur with GDP
two standard deviations or more below trend (which amounts to -9.2 percent below trend), while
Tomz and Wright found that 32 percent of defaults occur with GDP in the lowest quintile of
the distribution of GDP deviations from trend (which in their data corresponds to the range of
-11 to -7 percent below trend).
Column (3) of Table 2 shows the e¤ects of removing the exogenous component of capital ‡ows
xt . This has small e¤ects on most of the moments, except the correlation between net exports
and GDP and the mean spreads. Since xt can be viewed as an exogenous trade de…cit that is
perfectly correlated with TFP, removing it makes the trade balance less countercyclical. The
mean spreads change because we do not change any of the other parameters, and hence without
xt the probability of default increases to about 1 percent, and the mean spreads rise accordingly
because of the risk neutral lenders’ arbitrage condition. Thus, the exogenous component of
capital ‡ows plays a small role in our results, except for enabling the model to produce the trade
surplus regularly observed after default events.
4.3
Macroeconomic Dynamics around Default Events
We study the model’s ability to match output dynamics around default episodes by applying
event study techniques to simulated time series data. The left panel in Figure 7 plots the
model’s average path of output around default events together with the data for Argentina’s
HP detrended GDP around the 2002 default (1999Q1 to 2005Q3). The event window covers 12
30
quarters before and after debt defaults, with the default events normalized to date 0. We plot
the average for output in the model at each date t =
12; :::; 12 around default events in the
simulations. Hence, the simulated GDP line represents the average behavior of output around
defaults in the model’s stochastic stationary state. Since Argentina’s data is for a single default
event, instead of a long-run average, we add dashed lines with one-standard-error bands around
the model simulation averages.
4
2
percent deviation
percent deviation
5
0
-5
0
-2
-4
-6
-10
-12
-8
-8
-4
0
quarter
4
8
-10
-12
12
-8
-4
0
quarter
4
8
12
Model average
Continued exclusion
Immediate reentry
Data
Model average
Model one-std-error bands
Figure 7: Output around Default Events
The model’s mean output dynamics are a good match of those observed in the data. The
size of the output drop in the date of the default is matched by calibrating A, but the model also
tracks closely Argentina’s output dynamics before and after the default. Except for the quarter
just before the default, for which the model predicts higher output than in the data, output in
the data remains inside the model’s one-standard-error bands throughout the twenty-…ve quarter
event window.
Defaults in the model are triggered by adverse TFP shocks, but these shocks are not unusually
large. On average, TFP declines by 7.95 percent in the model’s default events, which is roughly
1.5 times of the 5.8 percent standard deviation of the calibrated TFP process (
" ).
Thus,
defaults occur with a TFP shock of just about 1.5 standard deviation in size, which suggests
that the model’s …nancial transmission mechanism ampli…es signi…cantly the real e¤ects of TFP
shocks when these shocks trigger default.
The ampli…cation e¤ect can be quanti…ed by computing the average output drop that the
model produces in response to a 7.95 percent TFP shock when there is no default, and comparing
it with the 13 percent mean output drop that the same shock produces when default occurs.
31
Without default, a 7.95 percent TFP shock produces a mean output drop of about 4.75 percent.
Thus, the ampli…cation coe¢ cient due to default is 13=4:75 = 2:73:
The recovery of output after defaults is driven by two e¤ects: First, since " is mean-reverting
and defaults occur with TFP below trend, TFP improves on average after defaults. Therefore,
even though the country remains in …nancial autarky on average for three years after a default,
the economy recovers because TFP improves. The second e¤ect is the surge in output that
occurs if the country re-enters credit markets (as …nal goods producers switch back to a more
e¢ cient mix of imported and domestic inputs). This can happen with 8.3 percent probability
every quarter.
These two e¤ects are illustrated in the right panel of Figure 7, which shows the simulated
paths of GDP with continued exclusion for 12 quarters after default and with immediate re-entry
one period after default. In the …rst scenario, the recovery re‡ects only the e¤ect of the mean
reversion of ". Since the probability of re-entry is low (at 8.3 percent), GDP in this exclusion
scenario is about the same as in the model average for about 7 quarters after default, but then
it moves below the model average because 8 quarters and beyond after a default the probability
of re-entry, with the associated e¢ ciency gain, starts to weigh more on the model average. In
contrast, the scenario with immediate re-entry shows a big rebound in GDP at t = 1; because
of the e¢ ciency gain that occurs in that period. The model average lies uniformly below the
immediate re-entry scenario because it always assigns some weigh to the continued exclusion
scenario, in which output is lower, and it generally weighs more the e¤ect of TFP recovery than
the e¤ect of credit market re-entry because of the low re-entry probability.
The model’s V-shaped output dynamics are qualitatively consistent with the data of emerging
markets that experienced Sudden Stops. Calvo, Izquierdo and Talvi (2006) conducted a crosscountry empirical analysis of the recovery of emerging economies from Sudden Stops, and found
that most recoveries are not associated with improvements in credit market access. In our model
as well, recovery occurs (on average) even though the economy continues to be excluded from
world credit markets. Notice, however, that the recovery without credit is always modest relative
to what occurs if credit market access is regained.
Figure 8 shows event windows that compare the actual default event dynamics from our
cross-country dataset (as shown in Figure 1) with the average of the model simulations, the
corresponding one-standard-error bands and also the data from Argentina’s 2002 default.33 The
plots show event windows for GDP, consumption, the trade balance-GDP ratio, imported inputs,
total intermediate goods, labor, the country interest rate and the debt-GDP ratio.
33
We provide both the cross-country medians and the observations for Argentina’s default because we aim to
illustrate how well the model can match both the behavior across the default events in our cross-country dataset
and the data for Argentina. The former is harder because the model’s calibration is based on Argentine data,
and thus misses cross-country variation in the model’s key parameters.
32
percent deviation
0 4
quarter
8 12
c. Trade balance/GDP
15
10
5
0
-12 -8 -4
0 4 8 12
quarter
e. Intermediate Goods
0
-10
-20
-3 -2 -1
0 1
year
2
3
percent deviation
-12 -8 -4
10
0
-10
percent deviation
-10
b. Consumption
-12 -8 -4
percent
percent
-12
0
-1
-3 -2 -1
0 1
year
f. Labor
2
3
0 1
year
2
3
1
0.9
0.8
-3 -2 -1
28
26
Error Band
100
24
-3 -2 -1
-8
-4
quarter
Model Mean
8 12
h. Debt/GDP*
Model in left axis, data in right axis
g. Interest Rate
15
10
5
0
0 4
quarter
d. Imported intermediate goods
1
indexed to t-4=1
0
percent deviation
percent deviation
a. GDP
10
Argentina
0 1
year
2
50
3
All-Country Median
Figure 8: Macro Dynamics around Default Events
Note: Consumption is H-P detrended. Trade balance and intermediate goods are computed
as the ratio of GDP and H-P detrended. For labor, imported inputs, total intermediate goods,
and debt, we aggregate the simulated data into annual frequency. Imported inputs and total
intermediate goods are log-linearly detrended. Labor is rescaled by the level of the corresponding
measure at 3 years before default. We take the annual data from Argentina and apply the same
procedure.
The scale for Argentine and cross-country median debt/GDP is drawn on the right axis.
33
The model does well at replicating the observed behavior of GDP, consumption and net
exports, in the sense that the actual paths of these variables are mostly within the model’s
standard error bands and close to the model averages. This is true for Argentina 2002 and for
the cross-country medians. The GDP and consumption drops that occur at t = 0 are larger
in the model than in the cross-country medians, but this is because Argentina’s recession was
larger than the median and we calibrated the model to match Argentina’s output collapse.
The model is consistent with the data in predicting a relatively stable path for net exports
before the default, a sudden increase around the default date and a sustained surplus after that.
The adjustment to include the exogenous component of capital ‡ows is important for the sudden
increase, but not for the stable trade balance before default. The rise in net exports when default
occurs is triggered by a low TFP realization "0 , which is associated with a surge in x0 . Without
this, net exports would go to zero at t = 0 and a small de…cit on average during the remainder
of the exclusion period, because during exclusion there would be no capital ‡ows to …nance a
trade imbalance (the average de…cit during exclusion would follow from averaging a zero trade
balance under …nancial autarky with a trade de…cit in case of re-entry to credit markets).
The qualitative features of the dynamics of imported inputs, total intermediate goods and
labor are also in line with the data. Quantitatively, however, the model predicts smaller declines
in labor and intermediate goods when defaults occur than in the data–with the caveat that
nontrivial data limitations in terms of country coverage and sample periods for these variables
makes them a weaker benchmark against which to compare the model’s dynamics. The drop
in imported inputs in the model is similar to the one observed in Argentina, but larger than
the cross-country median, re‡ecting again the fact that the model is calibrated to match the
recession in Argentina, which was larger than the cross-country median.
The model also does well at capturing the qualitative features of the dynamics of the interest
rate (inclusive of country risk) and the debt ratio, but quantitatively it tends to underestimate
both. The model produces a steady increase in the interest rate for the six quarters before
default.34 The debt ratio is relatively stable in the years before default, then surges with the
default, and drops in the years that follow.35 As explained earlier, interest rates in the model
are relatively low because they are pinned down by the default frequency, given the arbitrage
condition of risk neutral lenders, and the observed default frequency is low.The low debt ratio
is also in line with the previous result showing that while this model can support signi…cantly
higher debt ratios than existing models of sovereign default, it still underestimates actual debt
ratios.
34
As explained earlier, we do not show interest rates for t 0 because in the default state the default risk is
in…nite.
35
To make debt ratios comparable across data and model during periods of exclusion, we adjusted the model’s
measure to match the practice followed in the World Bank dataset, which includes defaulted debt and the corresponding interest in arrears in the debt estimates. Thus, the mean debt ratio for the model after default in the
event plot is the average of the pre-default debt ratio and the debt ratio chosen in the case of re-entry.
34
The sharp declines in GDP, consumption, labor and intermediate goods that occur when
access to credit markets is lost indicate that the model yields predictions consistent with the
Sudden Stops observed in emerging economies. In most of the Sudden Stops literature, however,
the loss of credit market access is modeled as the result of an exogenous shock, whereas in this
model the exclusion from credit markets and the economic collapse are endogenous and in‡uence
each other.36
4.4
Sensitivity Analysis
In this Section we conduct a sensitivity analysis to evaluate the robustness of the model’s key
quantitative predictions to changes in the range of imported inputs that require working capital
, the parameters of the Armington aggregator
and , the within-variety elasticity parameter
, the labor elasticity parameter !; and the re-entry probability . The results are summarized
in Table 4.37 This Table shows the main statistical moments we used to evaluate the performance
of the model for each alternative scenario, and also reproduces the statistics from the Argentine
data and the baseline model (see rows (1) and (2)).
(a)
Working capital
Rows (3)-(5) report results varying the value of . Row (3) removes working capital altogether
by setting
= 0, while rows (4) and (5) set
smaller ( = 0:6) and larger ( = 0:8) than the 0:7
baseline.
Without working capital, there is no output cost of default and no …nancial ampli…cation
e¤ect. Hence, to keep the results comparable with the other results in Table 4, in which default
is costly, and with those reported in quantitative studies of sovereign debt that use exogenous
proportional costs of default (e.g. Aguiar and Gopinath (2006), Yue (2010)), we introduce an
exogenous proportional cost of default when
= 0. This cost is set so that TFP falls by as much
as needed to produce an output drop of 13 percent when default occurs, which is the same size
as the drop in our baseline calibration. The other parameters are kept unchanged.
The model without working capital performs much worse than the baseline. In particular,
the frequency of defaults (proxied by the mean spread because of the lender’s risk neutrality)
falls from 0.7 to 0.05 percent, the variability of spreads also nearly vanishes, spreads become
procyclical, and the mean debt ratio drops to 9 percent. This marked worsening in the performance of the model follows from the fact that, without working capital, bond spreads no
longer a¤ect factor demands and production, and thus the cost of default becomes independent
of TFP. In short, this scenario shows that if we reduce our model to a variant of the standard
36
Mendoza (2010) proposed an alternative model of endogenous Sudden Stops based on collateral constraints
and Irving Fisher’s debt-de‡ation mechanism instead of sovereign default risk.
37
We also generated plots with the default event dynamics of output comparable to Figure 7. The quantitative
di¤erences are small and qualitatively they all have the same pattern, so we decided not to put them in the paper.
We also conducted the full sensitivity analysis without the exogenous component of capital ‡ows xt . Most of the
results are similar to those reported in Table 4, which again veri…es that xt plays a minor role, except for enabling
the model to produce the trade surplus after default.
35
Eaton-Gersovitz model with an exogenous proportional cost of default, we obtain results very
similar to what other authors have found.38
Table 4: Sensitivity Analysis
Output
Mean
Mean
Std.
GDP corr. with
frequency of
drop at
Debt/GDP
spread
dev of
spread
default w. GDP
default
ratio
default
spread
below trend
(1) Data
13%
35%
1.86%
0.78%
-0.62
-0.11
62%
(2) Baseline
13%
22.89%
0.71%
1.20%
-0.21
-0.10
86%
Working capital
(3)
=0
13%
8.99%
0.05%
0.08%
0.24
-0.02
75%
(4)
= 0:6
13.6%
20.38%
0.44%
0.88%
-0.12
-0.07
83%
(5)
= 0:8
14.44%
27.03%
0.39%
0.89%
-0.08
-0.07
96%
(6) 2:63 ( = 0:62)
15.46%
31.23%
0.53%
0.94%
-0.16
-0.09
88%
(7) 3:10 ( = 0:68)
12.20%
16.15%
0.91%
1.36%
-0.15
-0.10
80%
Armington elasticity
Armington share
(8)
= 0:58
16.30%
39.07%
0.28%
0.80%
-0.09
-0.07
77%
(9)
= 0:66
12.75%
14.19%
0.74%
1.21%
-0.18
-0.08
88%
Within-variety elasticity
(10) 2.22 ( = 0:55)
14.46%
25.94%
0.36%
0.84%
-0.07
-0.07
87%
(11) 2.89 ( = 0:65)
12.43%
19.77%
0.73%
1.17%
-0.12
-0.1
83%
Frisch elasticity of labor supply
(12) 1.67 (! = 1:6)
12.6%
22.34%
0.81%
1.22%
-0.16
-0.12
84%
(13) 2.5 (! = 1:4)
15.2%
24.35%
0.46%
1.06%
-0.03
-0.06
70%
Probability of re-entry
(14)
= 0:05
15.29%
37.23%
0.26%
0.71%
-0.12
-0.04
77%
(15)
= 0:1
13.85%
19.73%
0.61%
1.18%
-0.11
-0.07
89%
Row (5) shows that widening the range of imported input varieties that require working
capital to
= 0:8 (i.e. tightening the working capital constraint), instead of 0:7 as in the
baseline, increases the mean debt ratio by about 4.5 percentage points of GDP and generates
a larger output cost of default. The probability of default and the variability of spreads fall
by about 30 basis points, and the correlation between GDP and spreads increases to -0.08. If
instead we assume a narrower range of imported varieties that require working capital ( = 0:6),
Row (4) shows that we obtain a lower mean debt ratio than in the baseline, but the cost of
38
Note that the calibrated proportional drop in TFP is less than 1 percent in this experiment. If we set a
2 percent drop as in the literature, the output drop in default becomes 15 percent, the mean debt ratio is 24
percent, and the average spread falls to 0.01 percent, which are results in line with the literature (e.g. Aguiar and
Gopinath (2006)).
36
default and the correlation between GDP and spreads still rise, and the frequency of default
and the variability of spreads still fall, as in the case with
= 0:8. Hence, while rising
seems
to have a monotonic e¤ect increasing the mean debt ratio, the e¤ects on the other moments are
non-monotonic. This is because higher
has potentially opposing e¤ects on default incentives
and production plans. On one hand, since a larger fraction of imported inputs requires foreign
…nancing, changes in interest rates have a larger impact on production. This ampli…es the
response of output to productivity shocks, making output more volatile. On the other hand,
default can still lead to a higher output cost even with lower
default is larger with
= 0:6 than with
if the TFP shock that triggers
= 0:7. At the same time, the higher output cost of
default and GDP variability make it optimal for the sovereign to exercise the default option less
often, lowering the default probability and the volatility of bond spreads, and increasing the
mean debt/GDP ratio.
The distribution of defaults across “bad times”and “good times”also changes with the value
of . In particular, higher
annual frequency,
shifts the distribution toward states with GDP below trend. At the
= 0:8 implies that about 96 percent of defaults occur with output below
trend (compared with 86 percent in the baseline and 83 percent with
between GDP and default changes slightly to -0.07 with either
= 0:6). The correlation
= 0:8 or 0:6:
(b) Parameters of the Armington Aggregator of Domestic and Imported Inputs
Rows (6) and (7) report results for Armington elasticities lower (
(
md ;m
= 3:1) than the baseline (
md ;m
md ;m
= 2:63) and higher
= 2:9). Comparing the three scenarios, we …nd
predictable results from making domestic and imported inputs better substitutes, and in this
case the e¤ects are monotonic. As inputs become better substitutes, the output cost at default
and the mean debt ratio fall, and the frequency of default and the variability of the spreads
increase. The e¤ects of lowering the Armington share of domestic inputs to
or increasing it to
= 0:58 (Row (8))
= 0:66 (Row (9)), relative to the 0.62 baseline are similar: Increasing
makes the working capital channel operating via imported inputs less relevant, and as a result
the output cost at default and the mean debt ratio fall, and the frequency of default and the
variability of the spreads increase. Changes in
md ;m
and
have small e¤ects on business cycle
comovements. The correlations of GDP with spreads are slightly higher than in the baseline
case, but remain weakly negative.
It is worth noting that these variations
md ;m
and
result in expenditure ratios of imported
to domestic inputs that di¤er from those in the baseline and in the Mexican data used for
calibration. However, these expenditure ratios are still in the range of those for the countries
included in the study by Goldberg and Campa (2006), so scenarios like those in Rows (6)-(9)
should be regarded as plausible. Moreover, the range of expenditure ratios they documented
would also support a wider range of values of
md ;m
and
than those shown in Table 4,
including scenarios that can support very high debt ratios, albeit at lower default probabilities.
For example, using
= 0:5 we found a mean debt ratio of about 93 percent at a 0.2 percent
37
default frequency. Similarly, if we lower
to the threshold value at which imported and
md ;m
domestic inputs become gross complements (1.96), the mean debt ratio rises to 80 percent at a
negligible default frequency, and the output cost of default climbs to 22.6 percent.
Changing
md ;m
and
also a¤ects the distribution of default events across output realiza-
tions, but in this case the two parameters have e¤ects that go in opposite directions. Aggregating
again to annual frequency, the fraction of defaults that occurs with output below trend falls from
88 to 80 percent as we increase
we increase
md ;m
from 2.63 to 3.1, while it rises from 77 to 88 percent as
from 0.58 to 0.66. The correlations between GDP and default events change only
slightly.
(c) Within Elasticity of Imported Input Varieties
Rows (10) and (11) show results for lower (2.22) and higher (2.89) values of
mj
than the 2.44
baseline. Making imported input varieties better substitutes also weakens the working capital
channel, because it implies that the e¢ ciency loss of shifting away from the subset
inputs to its complement is smaller. Hence, as
mj
of imported
increases, the output drop at default and the
mean debt ratio fall, while the mean and standard deviation of spreads increase. The fraction
of defaults that occur with output below trend falls from 87 to 83 percent as
mj
rises from 2.22
to 2.89.
These e¤ects are again similar to those we obtained by increasing
they are weaker. In particular, we increased
basis points for
md ;m
mj
md ;m
, but quantitatively
by 62 basis points in Rows (10) and (11) v. 50
in Rows (6) and (7), and yet the changes in the cost of default, mean
debt ratio, mean and variability of spreads, and fraction of defaults with GDP below trend were
smaller in absolute value. This is in line with our previous …ndings from the partial equilibrium
analysis of the working capital mechanism, showing that changes in
md ;m
have larger e¤ects
on the responses of production and factor allocations to interest rate ‡uctuations than changes
in
mj .
Thus, for parameterizations around the baseline calibration, the Armington elastic-
ity of substitution across domestic and imported inputs a¤ects more the model’s quantitative
performance than the within elasticity across imported input varieties.
(d) Frisch Elasticity of Labor Supply
Rows (12) and (13) show results for lower (1.67) and higher (2.5) labor supply elasticities
than in the baseline (2.2). As we showed in Section 3, the e¢ ciency loss triggered by default is
larger the higher the elasticity of labor supply, because it implies that the labor market adjusts
to interest rate hikes with a smaller wage decline and a larger decline in total labor, which in
turn produce a smaller increase in Lm and a larger fall Lf . Hence, the output drop at default
and the mean debt ratio are bigger as we increase the elasticity of labor supply. At the same
time, the default probability (or the mean spread) and the variability of spreads fall with a
bigger labor elasticity. The change in labor elasticity also a¤ects the distribution of default
events across output realizations. The fraction of defaults with GDP below trend falls to 70
percent when the Frisch elasticity of labor supply is 2.5. The correlation between GDP again
38
increases slightly but remains weakly negative.
(e) Re-entry Probability (Mean Length of the Exclusion Period)
In Rows (14) and (15) we change the probability of re-entry to 5 and 10 percent respectively,
which imply exclusion periods of 5 and 2.5 years respectively (v. 3 years in the baseline). Here we
encounter again non-monotonic e¤ects. The output drop at default is higher, and the frequency
of default and the variability of spreads lower, when the mean exclusion period is either shorter
or longer than in the baseline. In contrast, the mean debt ratio does decline monotonically as
we lower the length of the exclusion period, from 37 percent with 5 years of exclusion to about
20 percent with 2.5 years. These results follow from the fact that increasing
has ambiguous
e¤ects on the value of default at date t (eq. (24)), by increasing the weigh of the re-entry
option at t + 1 but lowering the value of continuing in autarky. Intuitively, taking the default
option today becomes more attractive because credit market re-entry in the future is more likely
(i.e. "easier") but the expected value of staying in autarky is itself lower as the probability of
continuing in this state is lower.
The distribution of defaults also changes with the re-entry probability. The higher re-entry
probability shifts the distribution toward states with GDP below trend. At the annual frequency,
= 0:1 implies that about 89 percent of defaults occur with output below trend (compared with
86 percent in the baseline case). Yet for
= 0:05; the corresponding fraction is 77 percent. As
with the other scenarios, the correlations of GDP with defaults and with spreads increase slightly,
but remain weakly negative.
Summing up, this sensitivity analysis shows that while the model’s statistical moments vary
somewhat as we change key parameters, the main quantitative …ndings are robust to these
changes: The model produces large endogenous output drops at default as a result of the working capital channel, it produces higher mean debt ratios at higher default frequencies than is
generally the case in the quantitative sovereign debt literature, and generates weakly countercyclical spreads. The correlation between GDP and defaults remains slightly negative, and the
frequency of defaults with GDP below trend remains mostly in the 73-88 percent range. The
exception is the case in which the working capital channel is removed ( = 0 in Row (3)), which
removes the endogenous output cost of default. Replacing it with an exogenous proportional
cost calibrated to match the observed output drop, the model falls apart and can only generate
a small debt ratio at negligible levels of the default frequency and the variability of spreads, and
with pro-cyclical spreads.
5
Conclusions
This paper proposed an equilibrium model of sovereign default and business cycles and showed
that its quantitative predictions are broadly in line with observed empirical regularities. The
model features a …nancial ampli…cation mechanism that links default risk with production plans
39
and factor allocations via an e¢ ciency loss, because increases in default risk increase the …rms’
…nancing cost of working capital on a subset of imported inputs. This mechanism produces a
novel feedback loop between default risk, business cycles and the output cost of default.
In the model, producers of …nal goods choose an optimal mix of imported and domestic
inputs that are imperfect substitutes in an Armington aggregator, and varieties of imported
inputs that are also imperfect substitutes in a Dixit-Stiglitz aggregator. Some imported input
varieties require foreign working capital …nancing, and production of domestic inputs requires
reallocation of labor away from …nal goods production. In this setup, strategic default causes
an e¢ ciency loss because …nal goods producers cannot operate with the imported input varieties that require credit, substituting them for other imported inputs and domestic inputs, and
because labor reallocates from the …nal goods sector to the sector producing domestic inputs.
Lenders charge the same default risk premium on working capital loans as on sovereign debt
because the sovereign diverts the repayment of working capital loans when the country defaults.
These characteristics of the model are in line with empirical evidence on the substitution of
inputs around default episodes (e.g. Gopinath and Neiman (2010), the strong correlation between corporate and sovereign credit conditions (e.g. Arellano and Kocherlakota (2007)), and
the governments’assumption of foreign obligations of the private sector when sovereigns default
(e.g. Reinhart (2010)).
The model is broadly consistent with three key stylized facts of sovereign debt: (1) the
dynamics of macroeconomic aggregates around default events, (2) the negative correlation between interest rates on sovereign debt and output, and (3) high debt-output ratios on average
and when defaults take place. The model also explains key emerging markets business cycle
moments such as countercyclical net exports, high variability of private consumption, weakly
negative correlations between defaults and GDP, and the correlations of intermediate goods and
labor with spreads and GDP. Moreover, the results show that default occurs with adverse TFP
shocks that are not unusually large on average (about 1.5 times the standard deviation of TFP),
and that the model embodies a powerful …nancial ampli…cation mechanism that ampli…es the
e¤ect of TFP shocks on GDP by a factor of 2.7 in default events.
The model produces an endogenous output cost of default that is increasing in the state of
productivity. This is a key feature of the model that follows from the e¢ ciency loss induced by
the working capital channel, and from the convexity of marginal products with Cobb-Douglas
production. In this way, our model provides a foundation for the ad-hoc default cost (increasing
in endowment income above a threshold) that Arellano (2008) identi…ed as important in order
to induce default incentives that trigger default in bad states, at non-negligible debt ratios, and
at realistic default frequencies. In addition, the endogenous feedback between production and
default in our model produces a mean debt ratio four times larger than in Arellano’s model.
The model also provides a solution to the disconnect between sovereign debt models (which
rely on exogenous endowment dynamics with ad-hoc costs) and models of emerging markets
40
business cycles (which assume an exogenous …nancing cost of working capital calibrated to match
the interest rate on sovereign debt). In addition, the model o¤ers an interesting new perspective
on how structural features of the private sector and industrial and trade policies may interact
with sovereign debt ratios and default risk. The cost of default is lower in economies where
intermediate goods are better substitutes, where imported inputs are a smaller share of total
inputs (either because of the nature of technology or because of trade protection), or where
labor supply has a lower Frisch elasticity. As a result, economies with these characteristics
can support lower mean debt ratios at higher default frequencies. This may help explain why
the 1980s cluster of debt crises in Latin America a¤ected countries that engaged in import
substitution policies in the previous two decades.
We acknowledge, however, that the linkages between sovereign default and private sector
credit, and the mechanisms by which default induces e¢ ciency losses, should be the subject
of further research. For instance, introducing elements of political uncertainty, debt maturity,
secondary debt markets, dynamic renegotiation, and risk averse lenders, all of which have been
shown to add signi…cant elements to the analysis of sovereign default in models with exogenous
output dynamics, can be very promising lines of research (see, for example, Amador (2003), Benjamin and Wright (2008), Bi (2008a and 2008b), Broner, Martin and Ventura (2008), Chatterjee
and Eyigungor (2008), Cuadra and Sapriza (2008), D’Erasmo (2008), and Lizarazo (2005)).
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44
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45
Appendix 1: The Firms’ Dynamic Optimization Problem with
Working Capital
We review here the optimization problem faced by a representative …rm that needs working
capital to pay for a fraction of the cost of imported inputs. The setup is based on a similar
derivation in Uribe and Yue (2006). For simplicity, we characterize the problem in partial
equilibrium, assuming that all intermediate goods are imported, and that there is a single
homogeneous foreign input. We are interested in particular in the following two results:
1. The interest rate on within-period working capital loans is determined by the same rate
as the between-period rate of interest on one-period debt.
2. If …rms solve a standard problem to maximize the present value of pro…ts, they do not
accumulate precautionary asset holdings. In particular, if they start with zero liabilities,
they maintain zero liabilities at the end of each period in perpetuity.
Consider a representative …rm in a small open economy that produces output by means of a
production function that uses imported intermediate goods and labor as inputs,
yt = F (mt ; Lt );
(31)
where the function F is homogeneous of degree one, increasing in both arguments, and concave.
Firms buy their inputs from perfectly competitive markets.
Production is subject to a working capital constraint that requires …rms to pay in advance
for a fraction
of the cost of imported inputs, which have a world-determined relative price p.
The working capital constraint is:
t
Rt
where
t
pmt ;
0;
denotes the amount of working capital held by the representative …rm in period t.
The above formulation of the working capital constraint corresponds to a timing of transactions akin to a "cash-in- advance constraint," by which …rms must hold non-interest-bearing
foreign assets by an amount equal to the fraction
of the cost of imported inputs. There is also
an alternative formulation known as the "shopping time" formulation, according to which …rms
need to have the working capital pmt at the end of the period (see Uribe and Yue 2006 and
Oviedo 2005). The two di¤er only in that the former increases the cost of inputs by (Rt
as we show below, and the latter by
(Rt
1) ;
1) =Rt ; but in both cases the relevant interest rate
is determined by the same interest rate as for one-period debt Rt .
46
The debt position of the …rm, denoted by dt , evolves according to the following period-byperiod budget constraint:
d t = Rt
where
t
1 dt 1
F (mt ; Lt ) + wt Lt + pmt +
t
t 1
+
t;
denotes pro…ts in period t, and Rt is the interest rate in one-period bonds. Thus, there
is no assumption requiring that the interest rate on between period debt be the same as that on
working capital loans.
De…ne the …rm’s total net liabilities at the end of period t as at
Rt d t
t.
Then, we can
rewrite the budget constraint as:
at
= at
Rt
1
F (mt ; Lt ) + wt Lt + pmt +
t
+
Rt 1
Rt
t:
Assume the interest rate is positive at all times. This implies that the working capital constraint
always binds, or otherwise the …rm would incur in unnecessary …nancial costs, which would be
suboptimal. Since the working capital constraint holds with equality, we can eliminate
t
from
the above expression to get:
at
= at
Rt
1
F (mt ; Lt ) + pmt [1 + (Rt
1)] + wt Lt +
t:
(32)
The …rst result we highlighted earlier is evident in this expression: The working capital constraint
increases the unit cost of imported inputs by the amount (Rt
1), which is increasing in the
interest rate Rt , where Rt is the same interest rate as the one charged on one-period debt.
The …rm’s problem is to maximize the present discounted value of the stream of pro…ts. In the
paper the owners are domestic residents, so …rms discount at the households’stochastic discount
factor
t
t
0
, where
t
= R t Et
t+1
is the Euler equation for bond holdings. Alternatively, …rms
can be assumed to discount pro…ts at the world interest rates Rt . For the results we show here
this does not matter. Under the …rst alternative, the …rm’s problem is,
max E0
1
X
t=0
Using constraint (32) to eliminate
t
t
t
t:
0
from the …rm’s objective function, the …rm’s problem can
be stated as choosing at , mt , and Lt so as to maximize
E0
1
X
t=0
t
t
0
at
Rt
at
1
+ F (mt ; Lt )
pmt [1 + (Rt
at+j
s=0 Rt+s
subject to the no-Ponzi-game constraint limj!1 Et Qj
47
0:
1)]
wt Lt ;
The …rst-order conditions associated with this problem are the Euler equation for net liabilities,
t
= R t Et
t+1 ;
the no-Ponzi-game constraint holding with equality, and
Fm (mt ; Lt ) = p [1 + (Rt
1)]
(33)
FL (mt ; Lt ) = wt :
(34)
It is clear from condition (33) that the working capital requirement drives a wedge between the
marginal product of imported inputs and their world relative price p. This wedge is larger the
larger the …nancing cost of working capital, (Rt
1), or the higher the fraction of the cost of
imported inputs that needs to be paid with credit, .
It is critical to note that, since total net liabilities are irrelevant for the optimal choices
of labor and imported inputs and the payo¤ function of the …rm is linear with respect to net
liabilities (and all the terms in
t
= R t Et
t+1
are exogenous to the …rm’s choices), any process
at satisfying equation (32) and the …rm’s no-Ponzi-game constraint is optimal. Hence, if …rms
start out with zero net liabilities, then an optimal plan consists in holding no liabilities at all
times (at = 0 for all t
0), with distributed pro…ts given by
t
= F (kt ; ht )
pmt [1 + (Rt
1)]
wt Lt
This implies that …rms do not accumulate precautionary holdings of assets, regardless of the
input prices they face. Their choices of labor and imported inputs follow from the optimality
conditions (33)-(34), which depend only on current values of factor prices, the rate of interest
and TFP. These are not assumptions attached to the working capital requirement, but a result
that follows from the linear nature of the …rm’s payo¤: If …rms maximize the present value of
pro…ts, with discount rates independent of the …rm’s choices and net liabilities entering linearly in
pro…ts, there is no incentive for precautionary asset holdings by …rms. One can of course propose
alternative formulations that deviate from these conditions and would produce precautionary
asset demand by …rms, but these are not conditions assumed in the setup of the model.
Appendix 2: Decentralized Equilibrium
The social planner’s problem studied in Section 2 can be decentralized by formulating the problem of the sovereign as an optimal policy problem akin to a Ramsey problem.39 The government
chooses a debt policy (amounts and default or repayment) that maximizes the households’welfare given a bond pricing function qt (bt+1 ; "t ) and subject to the constraints that: (a) the private
sector allocations must be a competitive equilibrium; and (b) the government budget constraint
39
See Cuadra and Sapriza (2007) for an analysis of optimal …scal policy as a Ramsey problem in the presence
of sovereign default in an endowment economy.
48
must hold. The …rst constraint is dealt with by using conditions (14)-(20) to write down recursive functions that represent the competitive equilibria of factor allocations and factor prices as
functions of bond prices and TFP:
(qt (bt+1 ; "t ) ; "t ), M (qt (bt+1 ; "t ) ; "t ) ; m (qt (bt+1 ; "t ) ; "t ) ;
md (qt (bt+1 ; "t ) ; "t ) ; Lf (qt (bt+1 ; "t ) ; "t ) ; Lm (qt (bt+1 ; "t ) ; "t ), and L (qt (bt+1 ; "t ) ; "t ) ; recalling
that there is a one-to-one mapping between qt (bt+1 ; "t ) and rt : These functions are then entered
into the government’s optimization problem below.
This decentralization also requires an assumption about how the government deals with the
diverted repayment of working capital loans. This diverted repayment can be treated as a cost of
default, in which case we obtain the same allocations and prices in the decentralized equilibrium
as the planner’s problem of Section 2. Alternatively, if the government rebates the repayment as
a lump-sum transfer to households, the stock of working capital becomes an extra state variable,
because of the income e¤ect on households resulting from the transfer of the working capital
repayment when the country defaults. To consider both cases, in what follows we de…ne the
state variables of the government’s problem as (bt ;
t 1 ; "t ),
but
t 1
is only a relevant state if we
assume that diverted repayments of working capital are rebated to households. Note, however,
that since
t 1
is small in the calibration, our quantitative results change very little regardless
of whether we assume that these repayments are rebated or not.
The recursive optimization problem of the government is:
V (bt ;
t
n
;
"
)
=
max
v nd (bt ; "t ) ; v d (
1 t
t
o
"
)
:
1; t
The continuation value is de…ned as follows:
(
)
u
(c
g(L
(q
(b
;
"
)
;
"
)))
t
t
t+1
t
t
v nd (bt ; "t ) = max
;
ct ;bt+1
+ E [V (bt+1 ; (qt (bt+1 ; "t ) ; "t ) ; "t+1 )]
(35)
(36)
subject to
ct + qt (bt+1 ; "t ) bt+1
bt
"t f M (qt (bt+1 ; "t ) ; "t ) ; Lf (qt (bt+1 ; "t ) ; "t ) ; k
m (qt (bt+1 ; "t ) ; "t ) Pm
where f ( ) = M
M
(Lft )
L
1
qt (bt+1 ; "t )
1 ; (37)
k k : Note that the constraint of this problem is again the resource
constraint of the economy at a competitive equilibrium.
The working capital loans
t 1
and
t
do not enter explicitly in the continuation value or
in the resource constraint but they are relevant state variables, because the amount of working
capital loans taken by …nal goods producers at date t a¤ects the sovereign’s incentive to default
49
at t + 1. In particular, the value of default is:
d
v (
t 1 ; "t )
= max
ct
(
u ct
~ t ))
g(L("
) Ev d (0; "t+1 ) +
+ (1
EV (0; 0; "t+1 )
)
;
(38)
subject to:
~ ("t ) ; L
~ f ("t ) ; k
ct = "t f M
Note that v d (
t 1 ; "t )
m ("t ) P~ +
t 1:
(39)
takes into account the fact that in case of default at date t; the country
has no access to …nancial markets that period, and hence the country consumes the total income
given by the resource constraint in the default scenario. In this case, since …rms cannot borrow
~ ("), L(")
~
~ f (") are competitive equilibrium
to …nance the subset of imported inputs, M
and L
allocations that correspond to the case when the f sector operates without those inputs, and
1
R1
1
P~ =
pj
. Moreover, because the defaulting government diverts the repayment
dj
of last period’s working capital loans, household income includes government transfers equal to
the appropriated repayment
is Tt =
t 1
(i.e., on the date of default, the government budget constraint
t 1 ).
The default set is now de…ned as:
D (bt ;
t 1)
n
= "t : v nd (bt ; "t )
vd (
o
t 1 ; "t )
:
(40)
This default set has a di¤erent speci…cation than in the typical Eaton-Gersovitz model (see
Arellano (2008)), because the state of working capital a¤ects the gap between the values of
default and repayment. This results in a two-dimensional default set that depends on bt and
t 1,
instead of just bt : Despite of this, however, the probability of default remains a function
of bt+1 and "t only. This is because the f sector’s optimality conditions imply that the next
period’s working capital loan
t
depends on "t and the interest rate, which is a function of bt+1
and "t . Thus the probability of default at t + 1 perceived as of date t for a country with a
productivity "t and debt bt+1 , pt (bt+1 ; "t ), can be induced from the default set, the decision rule
for working capital, and the transition probability function of productivity shocks
follows:
pt (bt+1 ; "t ) =
Z
D(bt+1 ;
t)
d ("t+1 j"t ) , where
t
=
(qt (bt+1 ; "t ) ; "t ) :
("t+1 j"t ) as
(41)
To show the equivalence between the decentralized equilibrium when diverted working capital
repayments are not rebated and the planner’s problem of Section 2, consider …rst that, without
that rebate,
t 1
is removed from the set of state variables in the government’s problem, and
from the right-hand-side of the resource constraint when the country defaults. Next, consider
the fact that the recursive functions de…ned above to characterize factor allocations and prices
as functions of qt (bt+1 ; "t ) ; "t imply that conditions (14)-(20) hold. These are identical to the
50
…rst-order conditions that set factor allocations for the social planner in Section 2, and the
corresponding shadow prices of that planner’s problem determine the same wage rate and price of
domestic inputs. From these results it follows that, for given qt (bt+1 ; "t ) ; bt+1 and bt , the resource
constraints in the continuation and default branches are also identical in the two problems, which
therefore means that the value functions and optimal bond decision rules, assuming these are
well-de…ned, are also identical.
Appendix 3: Theorem Proofs
PROOF of THEOREM 1
Given a productivity shock ", the utility from defaulting v d ("0 ) is independent of b. We
can also show that the utility from not defaulting v nd (b; "0 ) is increasing in bt+1 . Therefore, if
V b1 ; "0 = v d ("0 ), then it must be the case that V b0 ; "0 = v d ("0 ). Hence, any "0 that belongs
in D b1 ; " must also belong in D b0 ; " .
Let d (b; "0 ) be the equilibrium default decision rule. The equilibrium default probability is
then given by
p (b; ") =
From D b1 ; "0
D b0 ; "0 , if d
R
d
b; "0 d
b1 ; "0 = 1, then d
p b0 ; "
"0 j" :
b0 ; "0 = 1. Therefore,
p b1 ; " :
PROOF of THEOREM 2
From Theorem 1, given a productivity shock " and b0 < b1
0, p
b0 ; "
p
b1 ; " . The
equilibrium bond price is given by
q b0 ; " =
p (b0 ; ")
:
1+r
1
Hence, using Theorem 1, we obtain that:
q b0 ; "
q b1 ; " :
Appendix 4: Data De…nition and Data Source
Table A1 describes the variables and data sources of our data set for cross-country event studies.
Table A2 summarizes the list of countries, default episodes, and the available variables in the
analysis.
The default episodes are based on Yeyati and Panizza (2011), Benjamin and Wright (2010),
and Standard and Poors report. Because we need the measure of economic variables which
typically re‡ect the impact of default with some lag, we use the quarter after the default an51
nouncement date in the event analysis. This treatment is the same as Yeyati and Panizza who
study the drop of GDP in the post-default quarters.
GDP, consumption, and trade balance/GDP are from International Financial Statistics and
Yeyati and Panizza(2011). Yeyati and Panizza(2011) compiled the real GDP for countries from
national sources for periods when IFS does not record their GDP. GDP, consumption, and trade
balance/GDP are H-P detrended.
The imported intermediate inputs are sum of categories for intermediate goods based on the
classi…cation of Broad Economic Categories (BEC). The categories for intermediate goods are:
(111*) Food and beverages, primary, mainly for industry, (121*) Food and beverages, processed,
mainly for industry, (21*) Industrial supplies not elsewhere speci…ed, primary, (22*) Industrial
supplies not elsewhere speci…ed, processed, (31*) Fuels and lubricants, primary, (322*) Fuels
and lubricants, processed (other than motor spirit), (42*) Parts and accessories of capital goods
(except transport equipment), (53*) Parts and accessories of transport equipment.
Intermediate goods are from United Nation, National Accounts O¢ cial Country Data. The
data is taken from Table 4.1 Total Economy (S.1), I. Production account - Uses Intermediate
consumption, at purchaser’s prices.
Labor data is the total paid employment data from LABORSTA dataset collected by International Labor Organization.
Because of the serious data limitation for imported inputs, total intermediate goods, and
labor, we cannot use HP …lter. Imported inputs and total intermediate goods are log-linearly
detrended. Labor data is indexed so that the employment 4 years before default is 1.
Table A1: Variables and Sources
Variable
De…nition
Frequency
Sources
International Financial Statistics
GDP
Real GDP
quarterly
CON
Real consumption
quarterly
International Financial Statistics
annual
United Nation comtrade (BEC code)
quarterly
International Financial Statistics
annual
United Nation
MS
TB
IM
Imported Intermediates
(in dollars, de‡ated by US PPI)
Trade Balance/GDP
Intermediate goods
(de‡ated by PPI)
and Yeyati and Panizza(2011)
L
Labor (paid employment)
annual
International Labor Organization
D
External debt/GNI
annual
Global Development Finance
S
Sovereign bond spreads
quarterly
EMBI+ and EMBI global (J.P. Morgan)
52
Table A2: List of countries and variables included in the event analysis.
Sovereign Default
Available series
Argentina 1982Q2
GDP, L, D
Argentina 2002Q1
GDP, CON, MS, TB, IM, L, D, S
Chile 1983Q1
GDP, D
Croatia 1992Q2
GDP, L
Domin. Rep. 1993Q1
GDP, D
Ecuador 1999Q3
GDP, CON, MS, TB, IM, D, S
Indonesia 1998Q3
GDP, CON, TB, D
Mexico 1982Q4
GDP, L, D
Moldova 2002Q1
GDP, CON, MS, L, TB, D
Nigeria 1983Q1
GDP, D
Nigeria 1986Q4
GDP, D
Pakistan 1998Q3
GDP, D
Peru 1983Q2
GDP, D
Philippines 1983Q4
GDP, CON, TB, D
Russia 1998Q4
GDP, CON, TB, IM, L, D, S
South Africa 1985Q4
GDP, CON, TB, L, D
South Africa 1993Q1
GDP, CON, TB, IM, L, D
Thailand 1998Q1
GDP, CON, MS, TB, D, S
Ukraine 1998Q4
GDP, MS, IM, L, D, S
Uruguay 1990Q2
GDP, D
Uruguay 2003Q2
GDP, MS, IM, L, D, S
Venezuela 1995Q3
GDP, IM, D, S
Venezuela 1998Q3
GDP, IM, D, S
53